Generation of equations for shell models of turbulence in the Maple system

The paper describes a technology for the automated compilation of equations for shell models of turbulence in the computer algebra system Maple. A general form of equations for the coefficients of nonlinear interactions is given, which will ensure that the required combination of quadratic invariants and power-law solutions is fulfilled in the model. Described the codes for the Maple system allowing to generate and solve systems of equations for the coefficients. The proposed technology allows you to quickly and accurately generate classes of shell models with the desired properties.

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Construction of complex shell models of MHD turbulence in computer algebra systems

E3S Web of Conferences ◽

10.1051/e3sconf/202019602008 ◽

2020 ◽

Vol 196 ◽

pp. 02008

Author(s):

Liubov Feshchenko ◽

Gleb Vodinchar

Keyword(s):

Conservation Laws ◽

Computer Algebra ◽

Nonlinear Interaction ◽

Power Distribution ◽

Computer Algebra System ◽

Stationary Solutions ◽

Computer Algebra Systems ◽

Mhd Turbulence ◽

Shell Models ◽

Shell Models Of Turbulence

The paper describes the developed by authors technique for construct-ing complex shell models of turbulence. The compilation of the equa-tions of this model and its exactly solution are implemented using by computer algebra system. The technique allows one to vary the sizes of nonlocality of nonlinear interaction in the space of scales, expressions for shell analogues of conservation laws, and the nature of stationary solutions with different power distribution.

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Application of computer algebra for the construction of shell models of turbulence

E3S Web of Conferences ◽

10.1051/e3sconf/201912702004 ◽

2019 ◽

Vol 127 ◽

pp. 02004

Author(s):

Liubov Feshchenko ◽

Gleb Vodinchar

Keyword(s):

Conservation Laws ◽

Computer Algebra ◽

Nonlinear Interaction ◽

Stationary Solutions ◽

Symbolic Calculation ◽

Shell Models ◽

Model Equations ◽

Shell Models Of Turbulence

The technique for automatic constructing of shell models of turbulence has been developed. The compilation of a model equations and its exactly solution is implemented using computer algebra (symbolic calculation) systems. The technique allows one to vary the scaling nonlocality of nonlinear interaction, form of expressions for conservation laws in models, and the form of stationary solutions with power distributions to scales.

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My Equations Are the Same as Yours!

Teaching Mathematics Online ◽

10.4018/978-1-60960-875-0.ch013 ◽

2012 ◽

pp. 259-273

Author(s):

M Badger ◽

C J Sangwin

Keyword(s):

Computer Algebra ◽

Computer Algebra System ◽

System Of Equations ◽

Systems Of Equations ◽

Computer Aided ◽

Two Systems

In this chapter we explain how computer aided assessment (CAA) can automatically assess an answer that consists of a system of equations. In particular, we will use a computer algebra system (CAS) and Buchberger’s Algorithm to establish when two systems of equations are the “same.”

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Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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