``Pseudo-invariant Eigen-operator" Method for Deriving Energy-Gap of an Atom-Cavity Jaynes–Cummings Hamiltonian with Atomic Centre-of-Mass Motion

2006 ◽  
Vol 45 (6) ◽  
pp. 1003-1006 ◽  
Author(s):  
Fan Hong-Yi ◽  
Tang Xu-Bing
2019 ◽  
Vol 14 (5) ◽  
pp. 658-666 ◽  
Author(s):  
Steffi L Colyer ◽  
Philip Graham-Smith ◽  
Aki IT Salo

Ground reaction forces produced on the blocks determine an athlete’s centre of mass motion during the sprint start, which is crucial to sprint performance. This study aimed to understand how force waveforms are associated with better sprint start performance. Fifty-seven sprinters (from junior to world elite) performed a series of block starts during which the ground reaction forces produced by the legs and arms were separately measured. Statistical parametric mapping (linear regression) revealed specific phases of these waveforms where forces were associated with average horizontal external power. Better performances were achieved by producing higher forces and directing the force vector more horizontally during the initial parts of the block phase (17–34% and 5–37%, respectively). During the mid-push (around the time of rear block exit: ∼54% of the block push), magnitudes of front block force differentiated performers, but orientation did not. Consequently, the ability to sustain high forces during the transition from bilateral to unilateral pushing was a performance-differentiating factor. Better athletes also exhibited a higher ratio of forces on the front block in the latter parts of unilateral pushing (81–92% of the block push), which seemed to allow these athletes to exit the blocks with lower centre of mass projection angles. Training should reflect these kinetic requirements, but also include technique-based aspects to increase both force production and orientation capacities. Specific training focused on enhancing anteroposterior force production during the transition between double- to single-leg propulsion could be beneficial for overall sprint start performance.


1979 ◽  
Vol 290 (3) ◽  
pp. 319-326 ◽  
Author(s):  
G. B�art ◽  
J. Deenen ◽  
G. Reidemeister
Keyword(s):  

2007 ◽  
Vol 21 (12) ◽  
pp. 1961-1969 ◽  
Author(s):  
HONG-YI FAN ◽  
TONG-TONG WANG

We show that the recently proposed invariant eigen-operator method is particularly applicable to solving the energy levels for some Hamiltonians in molecular physics. These are tri-atom molecules, the identical d-dimensional coupled harmonic oscillators and the dissipative linear-chain molecular model etc. The calculation is more direct and simpler than the usual diagonalization method for dynamic Hamiltonians.


1997 ◽  
Vol 40 (3) ◽  
pp. 263-268 ◽  
Author(s):  
M Löffler ◽  
G. M Meyer ◽  
H Walther

2018 ◽  
Vol 837 ◽  
pp. 819-838 ◽  
Author(s):  
J. B. Bostwick ◽  
P. H. Steen

A static rivulet is subject to disturbances in shape, velocity and pressure fields. Disturbances to interfacial shape accommodate a contact line that is either (i) fixed (pinned) or (ii) fully mobile (free) and preserves the static contact angle. The governing hydrodynamic equations for this inviscid, incompressible fluid are derived and then reduced to a functional eigenvalue problem on linear operators, which are parametrized by axial wavenumber and base-state volume. Solutions are decomposed according to their symmetry (varicose) or anti-symmetry (sinuous) about the vertical mid-plane. Dispersion relations are then computed. Static stability is obtained by setting growth rate to zero and recovers existing literature results. Critical growth rates and wavenumbers for the varicose and sinuous modes are reported. For the varicose mode, typical capillary break-up persists and the role of the liquid/solid interaction on the critical disturbance is illustrated. There exists a range of parameters for which the sinuous mode is the dominant instability mode. The sinuous instability mechanism is shown to correlate with horizontal centre-of-mass motion and illustrated using a toy model.


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