Construction of effective Hamiltonians for time‐dependent phenomena from variational principles

1991 ◽  
Vol 95 (5) ◽  
pp. 3607-3613 ◽  
Author(s):  
Julián Echave ◽  
Francisco M. Fernández ◽  
Mónica Campanaro ◽  
David A. Micha
Keyword(s):  
Variational Principles ◽  
Time Dependent ◽  
Effective Hamiltonians

Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model

2015 ◽  
Vol 5 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Variational Principles ◽  
Linear Time ◽  
Scale Effects ◽  
Time Dependent ◽  
Small Scale ◽  
Beam Model ◽  
Geometric Boundary ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

AbstractVariational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

On the equivalence of time-dependent variational principles

1988 ◽  
Vol 149 (5-6) ◽  
pp. 547-550 ◽  
Author(s):  
J. Broeckhove ◽  
L. Lathouwers ◽  
E. Kesteloot ◽  
P. Van Leuven
Keyword(s):  
Variational Principles ◽  
Time Dependent
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