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q-Gaussian approximants mimic non-extensive statistical-mechanical expectation for many-body probabilistic model with long-range correlations

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Thistleton W., Marsh J., Nelson K., Tsallis C.

Open Physics

2009

vol. 7

issue 3

387-394

We study a strictly scale-invariant probabilistic N-body model with symmetric, uniform, identically distributed random variables. Correlations are induced through a transformation of a multivariate Gaussian distribution with covariance matrix decaying out from the unit diagonal, as ρ/r α for r =1, 2, ..., N-1, where r indicates displacement from the diagonal and where 0 ⩽ ρ ⩽ 1 and α ⩾ 0. We show numerically that the sum of the N dependent random variables is well modeled by a compact support q-Gaussian distribution. In the particular case of α = 0 we obtain q = (1-5/3 ρ) / (1- ρ), a result validated analytically in a recent paper by Hilhorst and Schehr. Our present results with these q-Gaussian approximants precisely mimic the behavior expected in the frame of non-extensive statistical mechanics. The fact that the N → ∞ limiting distributions are not exactly, but only approximately, q-Gaussians suggests that the present system is not exactly, but only approximately, q-independent in the sense of the q-generalized central limit theorem of Umarov, Steinberg and Tsallis. Short range interaction (α > 1) and long range interactions (α < 1) are discussed. Fitted parameters are obtained via a Method of Moments approach. Simple mechanisms which lead to the production of q-Gaussians, such as mixing, are discussed.

Optimal Control Problem for a Conformable Fractional Heat Conduction Equation

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İskender Eroğlu B., Avcı D., Özdemir N.

Acta Physica Polonica A

2017

vol. 132

issue 3

658-662

This paper presents an optimal boundary temperature control of thermal stresses in a plate, based on time-conformable fractional heat conduction equation. The aim is to find the boundary temperature that takes thermal stress under control. The fractional Laplace and finite Fourier sine transforms are used to obtain the fundamental solution. Then the optimal control is held by successive iterations. Numerical results are depicted by plots produced by MATLAB codes.

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1 Acta Physica Polonica A

1 Open Physics

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1 Marsh J.

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1 Tsallis C.

1 Özdemir N.

1 İskender Eroğlu B.

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q-Gaussian approximants mimic non-extensive statistical-mechanical expectation for many-body probabilistic model with long-range correlations

Optimal Control Problem for a Conformable Fractional Heat Conduction Equation