Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier-Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant. (C) 2012 Elsevier Inc. All rights reserved.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems

This paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them. We propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points. The well known a priori meshes are compared with the proposed one. The comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes. A numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions. (C) 2015 Elsevier B.V. All rights reserved.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

No-reference image quality assessment using modified extreme learning machine classifier

In this paper, we present a machine learning approach to measure the visual quality of JPEG-coded images. The features for predicting the perceived image quality are extracted by considering key human visual sensitivity (HVS) factors such as edge amplitude, edge length, background activity and background luminance. Image quality assessment involves estimating the functional relationship between HVS features and subjective test scores. The quality of the compressed images are obtained without referring to their original images ('No Reference' metric). Here, the problem of quality estimation is transformed to a classification problem and solved using extreme learning machine (ELM) algorithm. In ELM, the input weights and the bias values are randomly chosen and the output weights are analytically calculated. The generalization performance of the ELM algorithm for classification problems with imbalance in the number of samples per quality class depends critically on the input weights and the bias values. Hence, we propose two schemes, namely the k-fold selection scheme (KS-ELM) and the real-coded genetic algorithm (RCGA-ELM) to select the input weights and the bias values such that the generalization performance of the classifier is a maximum. Results indicate that the proposed schemes significantly improve the performance of ELM classifier under imbalance condition for image quality assessment. The experimental results prove that the estimated visual quality of the proposed RCGA-ELM emulates the mean opinion score very well. The experimental results are compared with the existing JPEG no-reference image quality metric and full-reference structural similarity image quality metric.

Model Predictive Static Programming: A Computationally Efficient Technique For Suboptimal Control Design

Combining the philosophies of nonlinear model predictive control and approximate dynamic programming, a new suboptimal control design technique is presented in this paper, named as model predictive static programming (MPSP), which is applicable for finite-horizon nonlinear problems with terminal constraints. This technique is computationally efficient, and hence, can possibly be implemented online. The effectiveness of the proposed method is demonstrated by designing an ascent phase guidance scheme for a ballistic missile propelled by solid motors. A comparison study with a conventional gradient method shows that the MPSP solution is quite close to the optimal solution.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Load Transfer from a Smooth Elastic Pin to a Large Sheet

The plane problem of load transfer from an elastic interference or clearance fit pin to a large elastic sheet with a perfectly smooth interface is solved. As the load on the pin is monotonically increased, the pin-hole interface is in partial contact above certain critical load in interference fit and throughout the loading range in clearance fit.Such situations result in mixed boundary-value problems with moving boundaries and the arc of contact varies nonlinearly with applied load. These problems are analyzed by an inverse technique in which the arcs of contact/separation are prescribed and the causative loads are evaluated. A direct method of analysis is adopted using biharmonic polar trigonometric stress functions and a simple collocation method for satisfying the boundary conditions. A unified analytical formulation is achieved for interference and clearance fits. The solutions for the linear problem of push fits are inherent in the unified analysis. Numerical results highlighting the effects of pin and sheet elasticity parameters are presented.

The Alpha-Method Direct Transcription In Path Constrained Dynamic Optimization

Numerically discretized dynamic optimization problems having active inequality and equality path constraints that along with the dynamics induce locally high index differential algebraic equations often cause the optimizer to fail in convergence or to produce degraded control solutions. In many applications, regularization of the numerically discretized problem in direct transcription schemes by perturbing the high index path constraints helps the optimizer to converge to usefulm control solutions. For complex engineering problems with many constraints it is often difficult to find effective nondegenerat perturbations that produce useful solutions in some neighborhood of the correct solution. In this paper we describe a numerical discretization that regularizes the numerically consistent discretized dynamics and does not perturb the path constraints. For all values of the regularization parameter the discretization remains numerically consistent with the dynamics and the path constraints specified in the, original problem. The regularization is quanti. able in terms of time step size in the mesh and the regularization parameter. For full regularized systems the scheme converges linearly in time step size.The method is illustrated with examples.

Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

The concept of domain integral used extensively for J integral has been applied in this work for the formulation of J(2) integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the J(k) domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the J(k) integral. The proposed method is validated by solving standard problems with known solutions.

Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems. (C) 2004 Elsevier Ltd. All rights reserved.

2(n)-SEMA-a robust solid state nuclear magnetic resonance experiment for measuring heteronuclear dipolar couplings in static oriented systems using effective transverse spin-lock

Separated local field (SLF) spectroscopy is a powerful technique to measure heteronuclear dipolar couplings. The method provides site-specific dipolar couplings for oriented samples such as membrane proteins oriented in lipid bilayers and liquid crystals. A majority of the SLF techniques utilize the well-known Polarization Inversion Spin Exchange at Magic Angle (PISEMA) pulse scheme which employs spin exchange at the magic angle under Hartmann-Hahn match. Though PISEMA provides a relatively large scaling factor for the heteronuclear dipolar coupling and a better resolution along the dipolar dimension, it has a few shortcomings. One of the major problems with PISEMA is that the sequence is very much sensitive to proton carrier offset and the measured dipolar coupling changes dramatically with the change in the carrier frequency. The study presented here focuses on modified PISEMA sequences which are relatively insensitive to proton offsets over a large range. In the proposed sequences, the proton magnetization is cycled through two quadrants while the effective field is cycled through either two or four quadrants. The modified sequences have been named as 2(n)-SEMA where n represents the number of quadrants the effective field is cycled through. Experiments carried out on a liquid crystal and a single crystal of a model peptide demonstrate the usefulness of the modified sequences. A systematic study under various offsets and Hartmann-Hahn mismatch conditions has been carried out and the performance is compared with PISEMA under similar conditions.

A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.

Analysis of Long Cantilever Cylindrical Shell Subjected to Wind Loading

Bending analysis of closed cylindrical shells subjected to asymmetric load and having different support conditions is of interest in the design of chimneys, water towers, oil storage tanks, etc. A simple method of analyzing a long cantilever cylindrical shell, subjected to asymmetric load, is presented in the paper, using Schorer’s shell theory and orthogonal functions. The application of the solution has been illustrated with an example of a cantilever shell subjected to wind loads. The results obtained for this problem have been compared with the previously available results to illustrate the accuracy of the results obtained here. The solution presented can also be extended to a cylindrical shell with other support conditions, as well as to the study of free vibration of a cylindrical shell. The present solution will be very useful for designers who need to obtain numerical results for specific problems with minimum computational effort.

Analysis of clearance fit pin joints

The analysis of clearance fit joints falls within the realm of mixed boundary problems with moving boundaries. In this paper, this problem is solved by a simple continuum method of analysis applying an inverse technique; the region of contact is specified and the corresponding causative load is evaluated. Illustrations are given for a rigid clearance fit pin in a large elastic plate with smooth zero-shear interface between pin and plate, under biaxial plate stress at infinity and due to load transfer through pin.