Thickness-shear vibration of AT-cut quartz plates carrying finite-size particles with rotational degree of freedom and rotatory inertia [Correspondence]

2011 ◽  
Vol 58 (3) ◽  
pp. 666-670 ◽  
Author(s):  
Chunli Zhang ◽  
Nan Liu ◽  
Jiashi Yang ◽  
Weiqiu Chen
Keyword(s):  
Finite Size ◽  
Degree Of Freedom ◽  
Rotational Degree ◽  
Rotatory Inertia ◽  
Shear Vibration ◽  
Thickness Shear

Anomalous metallic-like transport of Co–Pd ferromagnetic nanoparticles cross-linked with π-conjugated molecules having a rotational degree of freedom

2014 ◽  
Vol 16 (1) ◽  
pp. 288-296 ◽  
Author(s):  
Yoshikazu Ito ◽  
Kazuyuki Takai ◽  
Akira Miyazaki ◽  
Vajiravelu Sivamurugan ◽  
Manabu Kiguchi ◽  
...  
Keyword(s):  
Degree Of Freedom ◽  
Ferromagnetic Nanoparticles ◽  
Rotational Degree ◽  
Conjugated Molecules

A Parameter to Quantify Molecular Quasilinearity

1976 ◽  
Vol 31 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Koichi Yamada ◽  
Manfred Winnewisser
Keyword(s):  
Physical Interpretation ◽  
Separation Of Variables ◽  
Degree Of Freedom ◽  
Rotational Degree ◽  
Vibrational Degree ◽  
Model Calculations ◽  
Linear Configuration ◽  
Oppenheimer Approximation ◽  
Linear Molecules ◽  
Simple Parameter

Abstract A simple parameter is proposed for expressing the quasilinearity of molecules in a quantitative way. The parameter γ0 is defined on the basis of a discussion of the separation of variables in the Born-Oppenheimer approximation. The parameter γ0 assumes the value +1 for bent molecules and -1 for linear molecules. The range from -1 to +1 traces the transition of a vibrational degree of freedom in the linear configuration of a polyatomic molecule into a rotational degree of freedom in the bent configuration. The sequence of molecules along this parameter is shown and model calculations are carried out to further illustrate the physical interpretation of the parameter.

scholarly journals CHAOTIC DYNAMICS OF N-DEGREE OF FREEDOM HAMILTONIAN SYSTEMS

2006 ◽  
Vol 16 (06) ◽  
pp. 1777-1793 ◽  
Author(s):  
CHRIS ANTONOPOULOS ◽  
TASSOS BOUNTIS ◽  
CHARALAMPOS SKOKOS
Keyword(s):  
Lyapunov Exponents ◽  
Hamiltonian Systems ◽  
Finite Size ◽  
Period Doubling ◽  
Power Laws ◽  
Degree Of Freedom ◽  
Einstein Condensation ◽  
Global Dynamics ◽  
Local And Global Dynamics ◽  
Very High

We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi–Pasta–Ulam (FPU) model and a discretized version of the nonlinear Schrödinger equation related to Bose–Einstein Condensation (BEC). We study solutions starting in the vicinity of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase motion (OPM), which are known in closed form and whose linear stability can be analyzed exactly. Our results verify that as the energy E increases for fixed N, beyond the destabilization threshold of these orbits, all positive Lyapunov exponents Li, i = 1,…, N - 1, exhibit a transition between two power laws, Li ∝ EBk, Bk > 0, k = 1, 2, occurring at the same value of E. The destabilization energy Ec per particle goes to zero as N → ∞ following a simple power-law, Ec/N ∝ N-α, with α being 1 or 2 for the cases we studied. However, using SALI, a very efficient indicator we have recently introduced for distinguishing order from chaos, we find that the two Hamiltonians have very different dynamics near their stable SPOs: For example, in the case of the FPU system, as the energy increases for fixed N, the islands of stability around the OPM decrease in size, the orbit destabilizes through period-doubling bifurcation and its eigenvalues move steadily away from -1, while for the BEC model the OPM has islands around it which grow in size before it bifurcates through symmetry breaking, while its real eigenvalues return to +1 at very high energies. Furthermore, the IPM orbit of the BEC Hamiltonian never destabilizes, having finite-size islands around it, even for very high N and E. Still, when calculating Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov exponents decrease following an exponential law and yield extensive Kolmogorov–Sinai entropies per particle h KS /N ∝ const., in the thermodynamic limit of fixed energy density E/N with E and N arbitrarily large.

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