Bond graph model of an induction machine with hysteresis nonlinearities

An induction machine is one of the most convenient devices for conversion of electrical energy to mechanical rotational energy. Induction machine is a typical member of a multi-domain, nonlinear, high-order dynamic system. To reduce its complexity, the mathematical models used for designing their control have several assumptions built into them. The most striking of these assumptions is that of linear magnetics. Bond graph is a convenient tool for modelling nonlinear elements. This paper proposes the use of the bond graph methodology to develop a model of an induction machine that includes the nonlinearities due to magnetics.     

A continuum mechanics approach for modelling arbitrary degradation and erosion processes in polymers

Composed of rather simple components some polymers show the ability to decompose from complex structures into substances that can be easily absorbed by the surrounding environment. The responsible processes behind chain shortening and eventually the material remove are degradation and erosion. The aim of this work is to model the chemo-mechanical condition of the polymer material based on a discretised network model. Further, the influence of erosion processes on the morphology is investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A hybrid data mining/simulation approach for modelling outpatient no-shows in clinic scheduling

This paper considers the outpatient no-show problem faced by a rural free clinic located in the south-eastern United States. Using data mining and simulation techniques, we develop sequencing schemes for patients, in order to optimize a combination of performance measures used at the clinic. We utilize association rule mining (ARM) to build a model for predicting patient no-shows; and then use a set covering optimization method to derive three manageable sets of rules for patient sequencing. Simulation is used to determine the optimal number of patients and to evaluate the models. The ARM technique presented here results in significant improvements over models that do not employ rules, supporting the conjecture that, when dealing with noisy data such as in an outpatient clinic, extracting partial patterns, as is done by ARM, can be of significant value for simulation modelling.     

The graph coloring problem: A neuronal network approach

Solution of an optimization problem with linear constraints through the continuous Hopfield network (CHN) is based on an energy or Lyapunov function that decreases as the system evolves until a local minimum value is attained. This approach is extended in to optimization problems with quadratic constraints. As a particular case, the graph coloring problem (GCP) is analyzed. The mapping procedure and an appropriate parameter-setting procedure are detailed. To test the theoretical results, some computational experiments solving the GCP are shown.     

Closed graph theorem: Topological approach

Some new types of Closed Graph Theorem are presented. These results generalize some theorems of T. Byczkowski, R. Pol and M. Wilhelm. An answer to a problem of M. Wilhelm is provided. This paper was completed while the second named author was a Visiting Professor at Young-stown State University.     

System theory: A new approach to wave mechanics

The intention of this paper is to show how the influence of the work of Bellman has initiated a tentative new approach to quantum mechanicsDedicated to R. Bellman     

A soft approach for hard continuous optimization

This paper is to introduce a soft approach for solving continuous optimizations models where seeking an optimal solution is theoretically or practically impossible.We first review methods for solving continuous optimization models, and argue that only a few optimization models with some good structure are solved. To solve a larger class of optimization problems, we suggest a soft approach by softening the goal in solving a model, and propose a two-stage process for implementing the soft approach. Furthermore, we offer an algorithm for solving optimization models with a convex feasible set, and verify the validity of the soft approach with numerical experiments.     

Multilevel graph partitioning: an evolutionary approach

The graph partitioning problem is defined as that of dividing the vertices of an undirected graph into a set of balanced parts through the removal of a set of edges, whose size is to be minimized. A number of researchers have investigated multilevel schemes, which coarsen the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partitioning of the original graph. In this paper, a genetic algorithm for the coarsening phase of a multilevel scheme for graph partitioning is presented. The proposed approach has been demonstrated to improve the solution quality at the expense of running time.     

A new computer-oriented approach to molecular mechanics

A new dynamical theory for atomic and molecular dynamics is formulated and discussed. The associated nonlinear differential system is derived from general atomic and molecular stability properties and from aspects of modern particle theory, especially as it relates to the structure of the electron. Computer experiments are described for developing a new model of the water molecule.     

A non-simultaneous variational approach for the oscillators with fractional-order power nonlinearities

This paper is concerned with a class of conservative oscillators the restitution force of which is of a power form which includes positive non-integer exponents. It is shown how an approximate Lagrangian and Hamilton’s variational principle can be used to obtain a second-order approximate solution for their free vibrations. Due to the fact that, in a general case, when the restoring force is multi-term, the period cannot be obtained from the energy conservation law in a closed form, the problem is formulated as a one-point boundary-value problem, and a non-simultaneous variation is introduced. The explicit expressions for the amplitudes and frequency of oscillations are derived, in which there are no restrictions on the values of the non-integer powers. The analytically obtained results are compared with numerical results as well as with some approximate analytical results from the literature.     

A semi-Markov approach for modelling asset deterioration

Considerable benefits have been gained from using Markov decision processes to select condition-based maintenance policies for the asset management of infrastructure systems. A key part of the method is using a Markov process to model the deterioration of condition. However, the Markov model assumes constant transition probabilities irrespective of how long an item has been in a state. The semi-Markov model relaxes this assumption. This paper describes how to fit a semi-Markov model to observed condition data and the results achieved on two data sets. Good results were obtained even where there was only 1 year of observation data.     

A graph theoretic approach to matrix inversion by partitioning

LetM be a square matrix whose entries are in some field. Our object is to find a permutation matrixP such thatPM P ^–1 is completely reduced, i.e., is partitioned in block triangular form, so that all submatrices below its diagonal are 0 and all diagonal submatrices are square and irreducible. LetA be the binary (0, 1) matrix obtained fromM by preserving the 0's ofM and replacing the nonzero entries ofM by 1's. ThenA may be regarded as the adjacency matrix of a directed graphD. CallD strongly connected orstrong if any two points ofD are mutually reachable by directed paths. Astrong component ofD is a maximal strong subgraph. Thecondensation D ^* ofD is that digraph whose points are the strong components ofD and whose lines are induced by those ofD. By known methods, we constructD ^* from the digraph,D whose adjacency matrixA was obtained from the original matrixM. LetA ^* be the adjacency matrix ofD ^*. It is easy to show that there exists a permutation matrixQ such thatQA ^* Q ^–1 is an upper triangular matrix. The determination of an appropriate permutation matrixP from this matrixQ is straightforward.This was an informal talk at the International Symposium on Matrix Computation sponsored by SIAM and held in Gatlinburg, Tennessee, April 24–28, 1961 and was an invited address at the SIAM meeting in Stillwater, Oklahoma on August 31, 1961     

The semiclassical approximation in quantum mechanics. A new approach

It is shown that the semiclassical approximation in quantum mechanics is equivalent to replacement of the Schrödinger equation by a finite closed system of first-order ordinary differential equations with initial conditions that satisfy special restrictions.Moscow Institute of Electronic Engineering; Tomsk State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 48–55, January, 1994.     

A new approach in modelling undesirable output in DEA model

With an increasing attention on the environment, one of the major research thrusts in Data Envelopment Analysis (DEA) based performance evaluation is the undesirable output in the conventional DEA model. There is considerable research published on the undesirable aspects of production outputs. However, the economic implications and the suitability of the DEA models for incorporating the undesirable outputs are less carefully investigated and discussed. In this paper, a comparative study is conducted of typical eco-DEA models to illustrate this issue. We propose a ratio model to evaluate the undesirable as well as the desirable outputs simultaneously. We apply the specially developed model to investigate the impact of production pollutants while conducting the efficiency evaluation in the textile industry of China. The results reveal that the production output-oriented efficiency evaluation can be significantly altered once the environmental aspects are factored into the model.     

A combined molecular dynamics-phase-field modelling approach to fracture

In order to better understand and ease the determination of material and model parameters required for the macroscopic modelling of brittle fracture, a bottom-up comparative study between molecular dynamics (MD) simulations and the continuum phase-field modelling (PFM) is carried out. In particular, based on the MD simulations of fracture of a highly brittle material, a number of PFM parameters such as the width of the transition zone between the damaged and the undamaged material, the crack resistance and the elasticity modulus are estimated. This study opens the door for an efficient way for multi-scale modelling of fracture. To illustrate this approach, a comparative two-dimensional numerical initial-boundary-value problem (IBVP) for the highly brittle aragonite (CaCO₃) is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)