Search results for: linear concentration gradient

Authors: Robert van Ling, Alexander Schwahn, Shanhua Lin, Ken Cook, Frank Steiner, Rowan Moore, Mauro de Pra

Abstract:

Purpose: Demonstration of fast high resolution charge variant analysis for monoclonal antibody (mAb) therapeutics within 5 minutes. Methods: Three commercially available mAbs were used for all experiments. The charge variants of therapeutic mAbs (Bevacizumab, Cetuximab, Infliximab, and Trastuzumab) are analyzed on a strong cation exchange column with a linear pH gradient separation method. The linear gradient from pH 5.6 to pH 10.2 is generated over time by running a linear pump gradient from 100% Thermo Scientific™ CX-1 pH Gradient Buffer A (pH 5.6) to 100% CX-1 pH Gradient Buffer B (pH 10.2), using the Thermo Scientific™ Vanquish™ UHPLC system. Results: The pH gradient method is generally applicable to monoclonal antibody charge variant analysis. In conjunction with state-of-the-art column and UHPLC technology, ultra fast high-resolution separations are consistently achieved in under 5 minutes for all mAbs analyzed. Conclusion: The linear pH gradient method is a platform method for mAb charge variant analysis. The linear pH gradient method can be easily optimized to improve separations and shorten cycle times. Ultra-fast charge variant separation is facilitated with UHPLC that complements, and in some instances outperforms CE approaches in terms of both resolution and throughput.

Keywords: charge variants, ion exchange chromatography, monoclonal antibody, UHPLC

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

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

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

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

Procedia PDF Downloads 115

Authors: M. Yaqub Khan, Usman Shabbir

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History of plasma reveals that continuous struggle of experimentalists and theorists are not fruitful for confinement up to now. It needs a change to bring the research through entropy. Approximately, all the quantities like number density, temperature, electrostatic potential, etc. are connected to entropy. Therefore, it is better to change the way of research. In ion temperature gradient mode with the help of Braginskii model, Boltzmannian electrons, effect of velocity shear is studied inculcating entropy in the magnetoplasma. New dispersion relation is derived for ion temperature gradient mode, and dependence on entropy gradient drift is seen. It is also seen velocity shear enhances the instability but in anomalous transport, its role is not seen significantly but entropy. This work will be helpful to the next step of tokamak and space plasmas.

Keywords: entropy, velocity shear, ion temperature gradient mode, drift

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Authors: Zhifeng Kong

Abstract:

Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: over-parameterization, rectified linear units ReLU, convergence, gradient descent, neural networks

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Authors: S. Khan, A. Khan, Abdul R. Soomrani, Raja F. Zafar, A. Waqas, G. Akbar

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This paper proposes a low-complexity image interpolation method. Image interpolation is used to convert a low dimension video/image to high dimension video/image. The objective of a good interpolation method is to upscale an image in such a way that it provides better edge preservation at the cost of very low complexity so that real-time processing of video frames can be made possible. However, low complexity methods tend to provide real-time interpolation at the cost of blurring, jagging and other artifacts due to errors in slope calculation. Non-linear methods, on the other hand, provide better edge preservation, but at the cost of high complexity and hence they can be considered very far from having real-time interpolation. The proposed method is a linear method that uses gradient orientation for slope calculation, unlike conventional linear methods that uses the contrast of nearby pixels. Prewitt edge detection is applied to separate uniform regions and edges. Simple line averaging is applied to unknown uniform regions, whereas unknown edge pixels are interpolated after calculation of slopes using gradient orientations of neighboring known edge pixels. As a post-processing step, bilateral filter is applied to interpolated edge regions in order to enhance the interpolated edges.

Keywords: edge detection, gradient orientation, image upscaling, linear interpolation, slope tracing

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Authors: Wei-Jong Yang, Yu-Siang Su, Pau-Choo Chung, Jar-Ferr Yang

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Moving object detection (MOD) is an important issue in advanced driver assistance systems (ADAS). There are two important moving objects, pedestrians and scooters in ADAS. In real-world systems, there exist two important challenges for MOD, including the computational complexity and the detection accuracy. The histogram of oriented gradient (HOG) features can easily detect the edge of object without invariance to changes in illumination and shadowing. However, to reduce the execution time for real-time systems, the image size should be down sampled which would lead the outlier influence to increase. For this reason, we propose the histogram of uniformly-oriented gradient (HUG) features to get better accurate description of the contour of human body. In the testing phase, the support vector machine (SVM) with linear kernel function is involved. Experimental results show the correctness and effectiveness of the proposed method. With SVM classifiers, the real testing results show the proposed HUG features achieve better than classification performance than the HOG ones.

Keywords: moving object detection, histogram of oriented gradient, histogram of uniformly-oriented gradient, linear support vector machine

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Authors: Minto Rattan, Tania Bose, Neeraj Chamoli

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The present paper investigates the effect of linear thermal gradient on the steady-state creep behavior of rotating isotropic disc using threshold stress based Sherby’s creep law. The composite discs made of aluminum matrix reinforced with silicon carbide particulate has been taken for analysis. The stress and strain rate distributions have been calculated for discs rotating at linear thermal gradation using von Mises’ yield criterion. The material parameters have been estimated by regression fit of the available experimental data. The results are displayed and compared graphically in designer friendly format for the above said temperature profile with the disc operating under uniform temperature profile. It is observed that radial and tangential stresses show minor variation and the strain rates vary significantly in the presence of thermal gradation as compared to disc having uniform temperature.

Keywords: creep, isotropic, steady-state, thermal gradient

Procedia PDF Downloads 237

Authors: Jose Neri, Fabrice Canto, Alastair Magnaldo, Laurent Guillerme, Vincent Dugas

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A miniaturized and automated approach for the volumetric titration of free nitric acid in U(VI) solutions is presented. Free acidity measurement refers to the acidity quantification in solutions containing hydrolysable heavy metal ions such as U(VI), U(IV) or Pu(IV) without taking into account the acidity contribution from the hydrolysis of such metal ions. It is, in fact, an operation having an essential role for the control of the nuclear fuel recycling process. The main objective behind the technical optimization of the actual ‘beaker’ method was to reduce the amount of radioactive substance to be handled by the laboratory personnel, to ease the instrumentation adjustability within a glove-box environment and to allow a high-throughput analysis for conducting more cost-effective operations. The measurement technique is based on the concept of the Taylor-Aris dispersion in order to create inside of a 200 μm x 5cm circular cylindrical micro-channel a linear concentration gradient in less than a second. The proposed analytical methodology relies on the actinide complexation using pH 5.6 sodium oxalate solution and subsequent alkalimetric titration of nitric acid with sodium hydroxide. The titration process is followed with a CCD camera for fluorescence detection; the neutralization boundary can be visualized in a detection range of 500nm- 600nm thanks to the addition of a pH sensitive fluorophore. The operating principle of the developed device allows the active generation of linear concentration gradients using a single cylindrical micro channel. This feature simplifies the fabrication and ease of use of the micro device, as it does not need a complex micro channel network or passive mixers to generate the chemical gradient. Moreover, since the linear gradient is determined by the liquid reagents input pressure, its generation can be fully achieved in faster intervals than one second, being a more timely-efficient gradient generation process compared to other source-sink passive diffusion devices. The resulting linear gradient generator device was therefore adapted to perform for the first time, a volumetric titration on a chip where the amount of reagents used is fixed to the total volume of the micro channel, avoiding an important waste generation like in other flow-based titration techniques. The associated analytical method is automated and its linearity has been proven for the free acidity determination of U(VI) samples containing up to 0.5M of actinide ion and nitric acid in a concentration range of 0.5M to 3M. In addition to automation, the developed analytical methodology and technique greatly improves the standard off-line oxalate complexation and alkalimetric titration method by reducing a thousand fold the required sample volume, forty times the nuclear waste per analysis as well as the analysis time by eight-fold. The developed device represents, therefore, a great step towards an easy-to-handle nuclear-related application, which in the short term could be used to improve laboratory safety as much as to reduce the environmental impact of the radioanalytical chain.

Keywords: free acidity, lab-on-a-chip, linear concentration gradient, Taylor-Aris dispersion, volumetric titration

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Authors: Nadia Ben Youssef, Aicha Bouzid

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Gradient estimation is one of the most fundamental tasks in the field of image processing in general, and more particularly for color images since that the research in color image gradient remains limited. The widely used gradient method is Di Zenzo’s gradient operator, which is based on the measure of squared local contrast of color images. The proposed gradient mechanism, presented in this paper, is based on the principle of the Di Zenzo’s approach using quaternion representation. This edge detector is compared to a marginal approach based on multiscale product of wavelet transform and another vector approach based on quaternion convolution and vector gradient approach. The experimental results indicate that the proposed color gradient operator outperforms marginal approach, however, it is less efficient then the second vector approach.

Keywords: gradient, edge detection, color image, quaternion

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Authors: Kuniyoshi Abe

Abstract:

Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.

Keywords: bi-conjugate gradient stabilized method, convergence speed, Krylov subspace methods, linear equations, parallel variant

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Authors: Vikram Saini, Lillie Dewan

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This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates.

Keywords: hard non-linearity, least square, parameter estimation, stochastic approximation gradient, Wiener model

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Authors: Adil A. Mohammed, Seif-Eddeen K. Fateen, Tamer S. Ahmed, Tarek M. Moustafa

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Falling film were widely used for gas-liquid absorption and reaction process. Modeling of falling film for oligomerization of ethylene reaction to linear alpha olefins is developed. Although there are many researchers discuss modeling of falling film in many processes, there has been no publish study the simulation of falling film for the oligomerization of ethylene reaction to produce linear alpha olefins. The Comsol multiphysics software was used to simulate the mass transfer with chemical reaction in falling film absorption process. The effect of concentration profile absorption of the products through falling thickness is discussed. The effect of catalyst concentration, catalyst/co-catalyst ratio, and temperature is also studied. For the effect of the temperature, as it increase the concentration of C4 increase. For catalyst concentration and catalyst/co-catalyst ratio as they increases the concentration of C4 increases, till it reached almost constant value.

Keywords: falling film, oligomerization, comsol mutiphysics, linear alpha olefins

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: constrained integer problems, enumerative search algorithm, Heuristic algorithm, Tunneling algorithm

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Authors: Sergey Kopysov, Nikita Nedozhogin, Leonid Tonkov

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The article presents a parallel iterative solver for large sparse linear systems which can be used on a heterogeneous platform. Traditionally, the problem of solving linear systems does not scale well on multi-CPU/multi-GPUs clusters. For example, most of the attempts to implement the classical conjugate gradient method were at best counted in the same amount of time as the problem was enlarged. The paper proposes the pipelined variant of the conjugate gradient method (PCG), a formulation that is potentially better suited for hybrid CPU/GPU computing since it requires only one synchronization point per one iteration instead of two for standard CG. The standard and pipelined CG methods need the vector entries generated by the current GPU and other GPUs for matrix-vector products. So the communication between GPUs becomes a major performance bottleneck on multi GPU cluster. The article presents an approach to minimize the communications between parallel parts of algorithms. Additionally, computation and communication can be overlapped to reduce the impact of data exchange. Using the pipelined version of the CG method with one synchronization point, the possibility of asynchronous calculations and communications, load balancing between the CPU and GPU for solving the large linear systems allows for scalability. The algorithm is implemented with the combined use of technologies: MPI, OpenMP, and CUDA. We show that almost optimum speed up on 8-CPU/2GPU may be reached (relatively to a one GPU execution). The parallelized solver achieves a speedup of up to 5.49 times on 16 NVIDIA Tesla GPUs, as compared to one GPU.

Keywords: conjugate gradient, GPU, parallel programming, pipelined algorithm

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Safwan Kanan, Jonathan Dewsbury, Gregory Lane-Serff

Abstract:

A salinity gradient solar pond is a free energy source system for collecting, converting and storing solar energy as heat. In this paper, the principles of solar pond are explained. A mathematical model is developed to describe and simulate heat and mass transfer behavior of salinity gradient solar pond. Matlab codes are programmed to solve the one dimensional finite difference method for heat and mass transfer equations. Temperature profiles and concentration distributions are calculated. The numerical results are validated with experimental data and the results are found to be in good agreement.

Keywords: finite difference method, salt-gradient solar-pond, solar energy, transient heat and mass transfer

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Authors: Tejeet Singh, Harmanjit Singh

Abstract:

Creep behavior of thick-walled functionally graded cylinder consisting of AlSiC and subjected to internal pressure and high temperature has been analyzed. The functional relationship between strain rate with stress can be described by the well-known threshold stress based creep law with a stress exponent of five. The effect of imposing non-linear particle gradient on the distribution of creep stresses in the thick-walled functionally graded composite cylinder has been investigated. The study revealed that for the assumed non-linear particle distribution, the radial stress decreases throughout the cylinder, whereas the tangential, axial and effective stresses have averaging effect. The strain rates in the functionally graded composite cylinder could be reduced to significant extent by employing non-linear gradient in the distribution of reinforcement.

Keywords: functionally graded material, pressure, steady state creep, thick-cylinder

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: H. J. Kim, G. C. Park, K. C. Kim, J. H. Shin

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Cavities are frequently found beneath conduits on pile foundations in old embankments. Cavity reduces seepage length significantly and consequently causes piping failure of embankments. Case studies of embankment failures indicate that the relative settlement between ground and pile supported-concrete conduit was the main reason of the cavity. In this paper, an attempt to simulate the cavity-induced piping failure mechanism was made using finite element numerical method. Piping potential is examined by carrying out parametric study for influencing factors such as cavity length, water level, and flow conditions. The concentration of hydraulic gradient adjacent to cavity was found. It is found that the hydraulic gradient close to the cavity exceeds considerably the critical hydraulic gradient causing piping. Piping failure potential due to the existence of cavity is evaluated and contour map for the potential risk of an embankment for piping failure is proposed.

Keywords: cavity, hydraulic gradient, levee, piping

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Authors: Phanida Phukoetphim, Asaad Y. Shamseldin

Abstract:

In this study, the novel Stochastic Gradient Boosting (SGB) combination method is addressed for producing daily river flows from four different rain-runoff models of Ohinemuri catchment, New Zealand. The selected rainfall-runoff models are two empirical black-box models: linear perturbation model and linear varying gain factor model, two conceptual models: soil moisture accounting and routing model and Nedbør-Afrstrømnings model. In this study, the simple average combination method and the weighted average combination method were used as a benchmark for comparing the results of the novel SGB combination method. The models and combination results are evaluated using statistical and graphical criteria. Overall results of this study show that the use of combination technique can certainly improve the simulated river flows of four selected models for Ohinemuri catchment, New Zealand. The results also indicate that the novel SGB combination method is capable of accurate prediction when used in a combination method of the simulated river flows in New Zealand.

Keywords: multi-model combination, rainfall-runoff modeling, stochastic gradient boosting, bioinformatics

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Authors: Stella Sten, Peter Hedström, Joakim Odqvist, Susanne Norgren

Abstract:

Two functionally graded cemented carbide samples have been produced by local addition of Titanium carbide (TiC) to a pressed Tungsten carbide and Cobalt, WC-10 wt% Co, green body prior to sintering, with the aim of creating a gradient in both composition and grain size in the as-sintered component. The two samples differ only by the in-going WC particle size, where one sub-micron and one coarse WC particle size have been chosen for comparison. The produced sintered samples had a gradient, thus a non-homogenous structure. The Titanium (Ti), Cobalt (Co), and Carbon (C) concentration profiles have been investigated using SEM-EDS and WDS; in addition, the Vickers hardness profile has been measured. Moreover, the Ti concentration profile has been simulated using DICTRA software and compared with experimental results. The concentration and hardness profiles show a similar trend for both samples. Ti and C levels decrease, as expected from the area of TiC application, whereas Co increases towards the edge of the samples. The non-homogenous composition affects the number of stable phases and WC grain size evolution. The sample with finer in-going WC grain size shows a shorter gamma (γ) phase zone and a larger difference in WC grain size compared to the coarse-grained sample. Both samples show, independent of the composition, the presence of abnormally large grains.

Keywords: cemented carbide, functional gradient material, grain growth, sintering

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Authors: Belloufi Mohammed, Sellami Badreddine

Abstract:

This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising.

Keywords: unconstrained optimization, three-term conjugate gradient, sufficient descent property, line search

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Authors: Jeries J. Abou-Hanna

Abstract:

Several techniques exist for determining stress-intensity factors in linear elastic fracture mechanics analysis. These techniques are based on analytical, numerical, and empirical approaches that have been well documented in literature and engineering handbooks. However, not all techniques share the same merit. In addition to overly-conservative results, the numerical methods that require extensive computational effort, and those requiring copious user parameters hinder practicing engineers from efficiently evaluating stress-intensity factors. This paper investigates the prospects of reducing the complexity and required variables to determine stress-intensity factors through the utilization of the stress gradient and a weighting function. The heart of this work resides in the understanding that fracture emanating from stress concentration locations cannot be explained by a single maximum stress value approach, but requires use of a critical volume in which the crack exists. In order to understand the effectiveness of this technique, this study investigated components of different notch geometry and varying levels of stress gradients. Two forms of weighting functions were employed to determine stress-intensity factors and results were compared to analytical exact methods. The results indicated that the “exponential” weighting function was superior to the “absolute” weighting function. An error band +/- 10% was met for cases ranging from a steep stress gradient in a sharp v-notch to the less severe stress transitions of a large circular notch. The incorporation of the proposed method has shown to be a worthwhile consideration.

Keywords: fracture mechanics, finite element method, stress intensity factor, stress gradient

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Authors: Mustafa Arda, Metin Aydogdu

Abstract:

Carbon nanotubes (CNTs) have many possible application areas because of their superior physical properties. Nonlocal Theory, which unlike the classical theories, includes the size dependency. Nonlocal Stress and Strain Gradient approaches can be used in nanoscale static and dynamic analysis. In the present study, torsional vibration of CNTs was investigated according to nonlocal stress and strain gradient theories. Effects of the small scale parameters to the non-dimensional frequency were obtained. Results were compared with the Molecular Dynamics Simulation and Lattice Dynamics. Strain Gradient Theory has shown more weakening effect on CNT according to the Stress Gradient Theory. Combination of both theories gives more acceptable results rather than the classical and stress or strain gradient theory according to Lattice Dynamics.

Keywords: torsional vibration, carbon nanotubes, nonlocal gradient theory, stress, strain

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: B. Sellami, Y. Laskri, M. Belloufi

Abstract:

Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, a new family of conjugate gradient method is proposed for unconstrained optimization. This method includes the already existing two practical nonlinear conjugate gradient methods, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. The numerical experiments are done to test the efficiency of the new method, which implies the new method is promising. In addition the methods related to this family are uniformly discussed.

Keywords: conjugate gradient method, global convergence, line search, unconstrained optimization

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Authors: Nor Zila Abd Hamid, Mohd Salmi M. Noorani

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This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: chaotic approach, phase space, Cao method, local linear approximation method

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Authors: B. Sellami, M. Belloufi

Abstract:

Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new two-parameter family of conjugate gradient methods for unconstrained optimization. The two-parameter family of methods not only includes the already existing three practical nonlinear conjugate gradient methods, but also has other family of conjugate gradient methods as subfamily. The two-parameter family of methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the two-parameter family of methods. The numerical results show that this method is efficient for the given test problems. In addition, the methods related to this family are uniformly discussed.

Keywords: unconstrained optimization, conjugate gradient method, line search, global convergence

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Authors: A. Selmi, A. Bisharat

Abstract:

Using Fourier transform and based on the Mindlin's 2^nd gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

Keywords: Eshelby tensor, Eshelby-like tensor, Green’s function, Mindlin’s 2nd gradient model, spherical inclusion

Procedia PDF Downloads 239