scholarly journals Equipartition of Energy Defines the Size–Thickness Relationship in Liquid-Exfoliated Nanosheets

ACS Nano ◽  
2019 ◽  
Vol 13 (6) ◽  
pp. 7050-7061 ◽  
Author(s):  
Claudia Backes ◽  
Davide Campi ◽  
Beata M. Szydlowska ◽  
Kevin Synnatschke ◽  
Ezgi Ojala ◽  
...  
Keyword(s):  
Equipartition Of Energy

The Debye theory of solid-state heat capacities

2021 ◽  
pp. 295-309
Author(s):  
Geoffrey Brooker
Keyword(s):  
High Temperature ◽  
Solid State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
Linear Chain ◽  
Heat Capacities ◽  
Debye Theory ◽  
State Heat ◽  
Equipartition Of Energy ◽  
Reasonable Step

“The Debye theory of solid-state heat capacities” gives a careful account of the Debye cut-off. We start by looking at a monatomic linear chain, leading to degrees of freedom and the equipartition of energy at the high-temperature (classical) limit. Reasonable approximations lead more naturally to the Born–von Karman model than to Debye, but Debye follows via a further reasonable step.

scholarly journals Equipartition of energy for waves in symmetric space

1991 ◽  
Vol 97 (2) ◽  
pp. 403-416 ◽  
Author(s):  
Thomas P Branson ◽  
Gestur 'Olafsson
Keyword(s):  
Symmetric Space ◽  
Equipartition Of Energy

scholarly journals Kolmogorov Unstable Stellar Oscillations

1983 ◽  
Vol 66 ◽  
pp. 297-321
Author(s):  
J. Perdang
Keyword(s):  
Numerical Analysis ◽  
Internal Resonance ◽  
Degrees Of Freedom ◽  
High Surface ◽  
Broad Band ◽  
Resonance Effects ◽  
Stellar Oscillations ◽  
Noise Type ◽  
Non Linear ◽  
Equipartition Of Energy

AbstractWe survey the mathematics of non-linear Hamiltonian oscillations with emphasis being laid on the more recently discovered Kolmogorov instability. In the context of radial adiabatic oscillations of stars this formalism predicts a Kolmogorov instability even at low oscillation energies, provided that sufficiently high linear asymptotic modes have been excited.Numerical analysis confirms the occurrence of this instability. It is found to show up already among the lowest order modes, although high surface amplitudes are then required (ǀδrǀ/R ~ 0.5 for an unstable fundamental mode – first harmonic coupling). On the basis of numerical evidence we conjecture that in the Kolmogorov unstable regime the enhanced coupling due to internal resonance effects leads to an equipartition of energy over all interacting degrees of freedom. We also indicate that the power spectrum of such oscillations is expected to display two components: A very broad band of overlapping pseudo-linear frequency peaks spread out over the asymptotic range, and a strictly non-linear 1/f-noise type component close to the frequency origin.It is finally argued that the Kolmogorov instability is likely to occur among non-linearly coupled non-radial stellar modes at a surface amplitude much lower than in the radial case. This lends support to the view that this instability might be operative among the solar oscillations.

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