Accuracy of the two-iteration spectral method for phase change problems

The accuracy of the solution of phase change problems using a spectral method is studied. Two iterations in the expansion are used to obtain the interface location of a solidification problem in semi-infinite domain. Asymptotic expansion of the current approach is compared to the existing analytical solution of the problem, and the validity of the expansion is studied. The results indicate the accuracy of a numerical application of the current approach to finite and semi-infinite geometries.     

Connectivity preserving transformations for higher dimensional binary images

An N-dimensional digital binary image (I) is a function I:Z^N→{0,1}. I is connected if and only if its black pixels and white pixels are each (3^N−1)-connected. I is only connected if and only if its black pixels are (3^N−1)-connected. For a 3-D binary image, the respective connectivity models are and . A pair of (3^N−1)-neighboring opposite-valued pixels is called interchangeable in a N-D binary image I, if reversing their values preserves the original connectedness. We call such an interchange to be a (3^N−1)-local interchange. Under the above connectivity models, we show that given two binary images of n pixels/voxels each, we can transform one to the other using a sequence of (3^N−1)-local interchanges. The specific results are as follows. Any two -connected 3-dimensional images I and J each having n black voxels are transformable using a sequence of O((c₁+c₂)n²) 26-local interchanges. Here, c₁ and c₂ are the total number of 8-connected components in all 2-dimensional layers of I and J respectively. We also show bounds on connectivity under a different interchange model as proposed in [A. Dumitrescu, J. Pach, Pushing squares around, Graphs and Combinatorics 22 (1) (2006) 37-50]. Next, we show that any two simply connected images under the , connectivity model and each having n black voxels are transformable using a sequence of O(n²) 26-local interchanges. We generalize this result to show that any two , -connected N-dimensional simply connected images each having n black pixels are transformable using a sequence of O(Nn²)(3^N−1)-local interchanges, where N>1.     

Evolution of the solidification front of a binary mixture

We perform a numerical study of two-dimensional solidification of a binary alloy. We employ a front-fixing transformation and develop a finite-difference numerical scheme, which is then used to simulate the evolution of an initially planar solidification front. The self-similar solution is taken as a base state for numerical investigation; the parameter choice corresponds to the case when the melt is constitutionally supercooled and the linear instability is expected. The perturbed interface takes the form of traveling waves with nonlinear growth rate, with the increased Stefan number causing the slow-down of solidification. Another important feature is the decay of perturbation when the time _t0$t_0$ at which the perturbation is imposed to the self-similar base solution is large enough, despite the fact that the system is expected to be linearly unstable. Finally, we provide a numerical investigation of the lowest value of _t0$t_0$ for which the perturbation decays in time and its dependence on Stefan number.     

A modified variable time step method for solving ice melting problem

A modified numerical method was used by authors for solving 1D Stefan problem. In this paper a modified method is proposed with difference formulae and different methods of calculating the variable time step, which are deduced from Taylor series expansions of different conditions at the boundary. Also an extrapolation formula for the solution at the first point at the right of the computational domain is proposed. The numerical results are compared with those obtained from other methods.     

On the refined integral method for the one-phase Stefan problem with time-dependent boundary conditions

Refined integral heat balance is developed for Stefan problem with time-dependent temperature applied to exchange surface. The method is applied to phase change in the half-plane and ordinary differential equation is obtained for the solid/liquid interface. The results are compared to those obtained by heat balance integral, perturbation and numerical methods.     

A note on scale transformations in the PROMETHEE V method

As already noted by Mavrotas et al. (2006), the PROMETHEE V method for multi-attribute analysis of portfolio problems will fail to include an item in a portfolio if it has a negative net flow with respect to other items, although adding such an item might actually improve the entire portfolio. However, the model formulated by Mavrotas et al. introduces a bias in favor of large portfolios because the PROMETHEE V method is sensitive to scale transformations. The present paper analyzes this effect and proposes a method to correct it.     

A meshless method for one-dimensional Stefan problems

The paper presents a new meshless numerical technique for solving one-dimensional problems with moving boundaries including the Stefan problems. The technique presented is based on the use of the delta-shaped functions and the method of approximate fundamental solutions (MAFS) firstly suggested for solving elliptic problems and for heat equations in domains with fixed boundaries. The numerical examples are presented and the results are compared with analytical solutions. The comparison shows that the method presented provides a very high precision in determining the position of the moving boundary even for a region that initially has zero thickness.     

A semi-analytical numerical method for solving evolution and elliptic partial differential equations

A new method for analyzing initial–boundary value problems for linear and integrable nonlinear partial differential equations (PDEs) has been introduced by one of the authors.     

A discrete particle swarm optimization method for feature selection in binary classification problems

This paper investigates the feature subset selection problem for the binary classification problem using logistic regression model. We developed a modified discrete particle swarm optimization (PSO) algorithm for the feature subset selection problem. This approach embodies an adaptive feature selection procedure which dynamically accounts for the relevance and dependence of the features included the feature subset. We compare the proposed methodology with the tabu search and scatter search algorithms using publicly available datasets. The results show that the proposed discrete PSO algorithm is competitive in terms of both classification accuracy and computational performance.     

A sharp interface model for phase transitions in crystals with linear elasticity

A model describing phase transitions coupled with diffusion and linear elasticity in crystals under isothermal conditions is introduced. The elastic deformation as well as the phase parameter are obtained directly by the minimization of the free energy. After stating the model, the existence of strong solutions is proved. Copyright © 2004 John Wiley & Sons, Ltd.     

A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method

Based on the Adomian decomposition method, a new analytical and numerical treatment is introduced in this research to investigate linear and non-linear singular two-point BVPs. The effectiveness of the proposed approach is verified by several linear and non-linear examples.     

A new imputation method for incomplete binary data

In data analysis problems where the data are represented by vectors of real numbers, it is often the case that some of the data-points will have “missing values”, meaning that one or more of the entries of the vector that describes the data-point is not observed. In this paper, we propose a new approach to the imputation of missing binary values. The technique we introduce employs a “similarity measure” introduced by Anthony and Hammer (2006) [1]. We compare experimentally the performance of our technique with ones based on the usual Hamming distance measure and multiple imputation.     

A new method for solving singular fourth-order boundary value problems with mixed boundary conditions

In [1], [2], [3], [4], [5], [6], [7] and [8], it is very difficult to get reproducing kernel space of problem (1). This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of fourth-order in the new reproducing kernel space. The numerical results are compared with both the exact solution and its n-order derived functions in the example. It is demonstrated that the new method is quite accurate and efficient for fourth-order problems.     

A method for obtaining transitive approximations of a binary relation

A binary relation R does not always possess the desirable property of transitivity. Consequently, this needs to be imposed artificially by deviating as little as possible from R. In this paper, three approaches to transitive approximation are analyzed within a common distance-based framework: exterior (transitive closure), interior (openings or maximal transitive sub-relations contained in R) and mixed (transitive fittings) approximation. Additionally, we propose a method for obtaining all these transitive approximations. The method is based on a distance function optimization framework that leads to straightforward goal programming models.     

A non-local boundary value problem method for parabolic equations backward in time

The ill-posed parabolic equation backward in time

     

A new method for solving a class of mixed boundary value problems with singular coefficient

In [1], [2], [3], [4], [5], [6] and [7], it is very difficult to deal with initial boundary value conditions. In this paper, we give a new method to deal with boundary value conditions, the main contribution of this paper is to put mixed boundary value conditions into reproducing kernel Hilbert space. The numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.     

A new error estimation approach based on fuzzy logic system for H-R adaptive boundary element method

Conventional adaptive boundary element method cannot be universally applied to solve many more problems than the subject it discussed, and different error estimation formulas need to be designed for varied problems. This paper put forward a new error analysis method based on the fuzzy logic system, which is able to make error estimation effectively using human expert experience, and solve the two classical elasticity problems in conjunction with the H-R adaptive boundary element method. Numerical examples have illustrated the effectiveness, superiority and potential of a fuzzy logic approach in the adaptive boundary element method.     

A new Jacobi-like method for joint diagonalization of arbitrary non-defective matrices

This paper addresses the problem of joint diagonalization of a set of matrices. A new Jacobi-Like method that has the advantages of computational efficiency and of generality is presented. The proposed algorithm brings the general matrices into normal ones and performs a joint diagonalization by a combination of unitary and shears (non-unitary) transformations. It is based on the iterative minimization of an appropriate cost function using generalized Jacobi rotation matrices.