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Why Instantaneous Values of the “Covariant” Lyapunov Exponents Depend upon the Chosen State-Space Scale

Hoover W. G., Hoover C. G.

Computational Methods in Science and Technology

2014

Vol. 20, No. 1

5--8

We explore a simple example of a chaotic thermostated harmonic-oscillator system which exhibits qualitatively different local Lyapunov exponents for simple scale-model constant-volume transformations of its coordinate q and momentum p: {q, p} ! {(Q/s), (sP)}. The time-dependent thermostat variable ζ(t) is unchanged by such scaling. The original (qpζ) motion and the scale-model (QPζ) version of the motion are physically identical. But both the local Gram-Schmidt Lyapunov exponents and the related local “covariant” exponents change with the change of scale. Thus this model furnishes a clearcut chaotic time-reversible example showing how and why both the local Lyapunov exponents and covariant exponents vary with the scale factor s.

Wpływ optymalnego zasilania parownika na współczynnik COP urządzenia chłodniczego

Andrzejczyk R.

Technika Chłodnicza i Klimatyzacyjna

2011

nr 6-7

323-326

Symplectic and time reversible integrator for rigid bodies

Kamberaj H., Low R.J., Neal M.P.

Systems Science

2003

Vol. 29, nr 2

31-45

A symplectic and time-reversible molecular dynamics algorithm is presented for rigid molecules in the quaternion representation. The algorithm is developed on the basis of the Trotter factorisation scheme using a Hamiltonian formalism The structure is similar to that of the velocity Verlet algorithm. Subsequently we describe the coupling of the rigid bodies to a thermostat. The isothermal molecular dynamics is defined by introducing additional pseudo-friction coefficients, according to a generalised Nose-Hoover prescription.