Mathematical computer programs: A compilation

Computer programs, routines, and subroutines for aiding engineers, scientists, and mathematicians in direct problem solving are presented. Also included is a group of items that affords the same users greater flexibility in the use of software

Bifurcation structure of two Coupled Periodically driven double-well Duffing Oscillators

The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state in linear response, and classify the different types of bifurcation likely to occur in this model. We then explore the complex behaviour associated with these bifurcations numerically. Our results show many striking departures from the behaviour of coupled driven Duffing Oscillators with single well-potentials, as characterised by Kozlowski et al \cite{k1}. In addition to the well known routes to chaos already encountered in a one-dimensional Duffing oscillator, our model exhibits imbricated period-doubling of both types, symmetry-breaking, sudden chaos and a great abundance of Hopf bifurcations, many of which occur more than once for a given driving frequency. We explore the chaotic behaviour of our model using two indicators, namely Lyapunov exponents and the power spectrum. Poincar\'e cross-sections and phase portraits are also plotted to show the manifestation of coexisting periodic and chaotic attractors including the destruction of $T^2$ tori doubling.Comment: 16 pages, 8 figure

A short note on a generalization of the Givens transformation

A new transformation, a generalization of the Givens rotation, is introduced here. Its properties are studied. This transformation has some free parameters, which can be chosen to attain pre-established conditions. Some special choices of those parameters are discussed, mainly to improve numerical properties of the transformation. © 2013 Elsevier Ltd. All rights reserved.A new transformation, a generalization of the Givens rotation, is introduced here. Its properties are studied. This transformation has some free parameters, which can be chosen to attain pre-established conditions. Some special choices of those parameters6615661CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOSEM INFORMAÇÃOSEM INFORMAÇÃOBjörck, A., (1996) Numerical Methods for Least Squares Problems, , SIAM PhiladelphiaGolub, G.H., Loan, C.V., (1996) Matrix Computation, , 3rd Edition The Johns Hopkins University Press Baltimore and LondonStewart, G.W., (1973) Introduction to Matrix Computations, , Academic Press New YorkStewart, G.W., (1998) Matrix Algorithms I: Basic Decompositions, , SIAM PhiladelphiaBai, Z., Demmel, J., Dongarra, J., Ruhe, A., Van Der Vorst, H., (2000) Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, , SIAM PhiladelphiaGolub, G.H., (1999) Numerical Methods for Large Scale Eigenvalue Problems, Teaching Note, , Stanford UniversityParlette, B., (1997) The Symmetric Eigenvalue Problem, 20. , Reprinted as Classics in Applied Mathematics SIAM PhiladelphiaStewart, G.W., (2001) Matrix Algorithms II: Eigensystems, , SIAM PhiladelphiaGerck, E., D'Oliveira, A.B., Continued fraction calculation of the eigenvalues of tridiagonal matrices arising from the Schrödinger equation (1980) Journal of Computational and Applied Mathematics, 6, pp. 81-82Golub, G.H., Robertson, N.T., A generalized Bairstow algorithm (1967) Communication on Applied and Computational Mathematics, 10, pp. 371-373Im, Y., Ri, S., An algorithm for the calculation of eigenvalues of tridiagonal matrices using QD-transformations and the LR (RL) method (1995) Su-hak: Academy of Science of the People's Democratic Republic of Korea, 2, pp. 12-15Kulkarni, D., Schmidt, D., Tsui, S.K., Eigenvalues of tridiagonal pseudo-toeplitz matrices (1999) Linear Algebra and Its Applications, 297Pasquini, L., Pavani, R., Computing the eigenvalues of non-normal tridiagonal matrices (1995) Rendiconti Del Seminario Matematico e Fisico di Milano, 65, pp. 109-138Veselic, K., On real eigenvalues of real tridiagonal matrices (1979) Linear Algebra and Its Applications, 27, pp. 167-171Golub, G.H., Yuan, J.Y., Biloti, R., Ramos, J., Optimal generalized Householder transformation with application (2005) Tech. Rep., Universidade Federal Do Paraná, , BrazilLabudde, C.D., The reduction of an arbitrary real square matrix to tridiagonal form using similarity transformations (1963) Mathematics of Computation, 17, pp. 433-437Stathopolous, A., Saad, Y., Wu, K., Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods (1998) SIAM Journal on Scientific Computing, 19, pp. 227-24

Modeling Joint Survival Probabilities of Runs Scored and Balls Faced in Limited Overs Cricket Using Copulas

In limited overs cricket, the goal of a batsman is to score a maximum number of runs within a limited number of balls. Therefore, the number of runs scored and the number of balls faced are the two key statistics used to evaluate the performance of a batsman. In cricket, as the batsmen play as pairs, having longer partnerships is also key to building strong innings. Moreover, having a steady opening partnership is extremely important as a team aims to build such a stronger innings. In this study, we have shown a way to evaluate the performance of opening partnerships in Twenty20 (T20) cricket and the performance of individual batsmen in One Day International Cricket (ODI) by modeling the joint distribution of runs scored and balls faced using copula functions. The joint survival probabilities derived from this approach are then used to evaluate the batting performance of opening partnerships and individual batsmen for different stages of the innings. Results of the study have shown that cricket managers and team officials can use the proposed method in selecting appropriate partnership pairs and individual batsmen in an efficient manner for specific situations in the match

Dopant-Dopant Interactions in Beryllium doped Indium Gallium Arsenide: an Ab Initio Study

We present an ab initio study of dopant-dopant interactions in beryllium-doped InGaAs. We consider defect formation energies of various interstitial and substitutional defects and their combinations. We find that all substitutional-substitutional interactions can be neglected. On the other hand, interactions involving an interstitial defect are significant. Specially, interstitial Be is stabilized by about 0.9/1.0 eV in the presence of one/two BeGa substitutionals. Ga interstitial is also substantially stabilized by Be interstitials. Two Be interstitials can form a metastable Be-Be-Ga complex with a dissociation energy of 0.26 eV/Be. Therefore, interstitial defects and defect-defect interactions should be considered in accurate models of Be doped InGaAs. We suggest that In and Ga should be treated as separate atoms and not lumped into a single effective group III element, as has been done before. We identified dopant-centred states which indicate the presence of other charge states at finite temperatures, specifically, the presence of Beint+1 (as opposed to Beint+2 at 0K)

Stable predictor-corrector methods for first order ordinary differential equations

Because of the wide variety of differential equations, there seems to be no numerical method which will affect the solution best for all problems. Predictor-corrector methods have been developed which utilize more ordinates in the predictor and corrector equations in the search for a better method. These methods are compared for stability and convergence with the well known methods of Milne, Adams, and Hamming --Abstract, page ii

Flutter analysis using transversality theory

A new method of calculating flutter boundaries of undamped aeronautical structures is presented. The method is an application of the weak transversality theorem used in catastrophe theory. In the first instance, the flutter problem is cast in matrix form using a frequency domain method, leading to an eigenvalue matrix. The characteristic polynomial resulting from this matrix usually has a smooth dependence on the system's parameters. As these parameters change with operating conditions, certain critical values are reached at which flutter sets in. Our approach is to use the transversality theorem in locating such flutter boundaries using this criterion: at a flutter boundary, the characteristic polynomial does not intersect the axis of the abscissa transversally. Formulas for computing the flutter boundaries and flutter frequencies of structures with two degrees of freedom are presented, and extension to multi-degree of freedom systems is indicated. The formulas have obvious applications in, for instance, problems of panel flutter at supersonic Mach numbers