Semiclassical dynamics in up to 15 coupled vibrational degrees of freedom

1997 ◽  
Vol 106 (12) ◽  
pp. 4832-4839 ◽  
Author(s):  
Mark L. Brewer ◽  
Jeremy S. Hulme ◽  
David E. Manolopoulos
Keyword(s):  
Degrees Of Freedom ◽  
Semiclassical Dynamics

scholarly journals Hidden Nambu mechanics II: Quantum/semiclassical dynamics

2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Atsushi Horikoshi
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Hamiltonian Dynamics ◽  
Extended Phase ◽  
Nambu Mechanics ◽  
Mechanical Structure ◽  
Wave Packet Dynamics ◽  
Semiclassical Dynamics ◽  
Metastable Potential

Abstract Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is hidden in Hamiltonian dynamics, that is, the classical time evolution of variables including redundant degrees of freedom can be formulated as Nambu mechanics. In the present paper we show that the Nambu mechanical structure is also hidden in some quantum or semiclassical dynamics, that is, in some cases the quantum or semiclassical time evolution of expectation values of quantum mechanical operators, including composite operators, can be formulated as Nambu mechanics. We present a procedure to find hidden Nambu structures in quantum/semiclassical systems of one degree of freedom, and give two examples: the exact quantum dynamics of a harmonic oscillator, and semiclassical wave packet dynamics. Our formalism can be extended to many-degrees-of-freedom systems; however, there is a serious difficulty in this case due to interactions between degrees of freedom. To illustrate our formalism we present two sets of numerical results on semiclassical dynamics: from a one-dimensional metastable potential model and a simplified Henon–Heiles model of two interacting oscillators.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

Das Experten-Novizen-Paradigma und die Vertrauenskrise in der Psychologie

2016 ◽  
Vol 23 (4) ◽  
pp. 131-140 ◽  
Author(s):  
Philip Furley ◽  
Karsten Schul ◽  
Daniel Memmert
Keyword(s):  
Degrees Of Freedom

Zusammenfassung. Das Ziel des vorliegenden Beitrages ist es anhand eines vielverwendeten Paradigmas in der Sportwissenschaft – dem Experten-Novizen-Vergleich – zu prüfen, ob die momentane Vertrauenskrise in der Psychologie ebenfalls die Sportpsychologie betreffen könnte. Anhand einer exemplarischen Studie zeigen wir, dass es innerhalb dieses Paradigmas zu kontroversen Befunden kommt, welche durch die vermuteten Ursachen der Vertrauenskrise (Researcher Degrees of Freedom, kleine Stichprobengrößen) erklärt sein könnten. Zusätzlich argumentieren wir, dass weitere Faktoren (Konfundierung, Stichprobengrößen, Rosenthal Effekt, Expertise-Definition) innerhalb dieses Paradigmas die Reproduzierbarkeit von Erkenntnissen in Frage stellen. Wir diskutieren mögliche Maßnahmen, wie die dargestellten Probleme des Experten-Novizen-Paradigmas in zukünftigen Forschungsarbeiten gelöst werden können.

Determination of Graft Forces for Cranial Cruciate Ligament Reconstruction in the Dog

1996 ◽  
Vol 09 (04) ◽  
pp. 165-171 ◽  
Author(s):  
D. A. Hulse ◽  
M. R. Slater ◽  
J. F. Hunter ◽  
W. A. Hyman ◽  
B. A. Shelley
Keyword(s):  
Degrees Of Freedom ◽  
Cruciate Ligament ◽  
Insertion Site ◽  
Graft Fixation ◽  
Flexion Angle ◽  
Patellar Ligament ◽  
Graft Material ◽  
Test Apparatus ◽  
Cranial Cruciate Ligament ◽  
Tibial Insertion

SummaryA test apparatus that allowed the stifle to move in five degrees of freedom was used to determine the effect of graft location, graft preload, and flexion angle at the time of graft fixation on the tensile graft forces experienced by a replacement graft material used to simulate reconstruction of the cranial cruciate ligament deficient stifle. Two graft locations (tibial insertion site of the patellar ligament and tibial insertion site of the cranial cruciate ligament), two graft preloads (5 N and 20 N), and three flexion angles at the time of graft fixation (15°, 30° and 90°) were examined. The tibial insertion site and preload did not have as great an effect on graft force as did the flexion angle of the limb at time of graft fixation. Graft forces were highest when reconstructions were performed with the limb in 90° of flexion (ρ <0.0001). This study supports the notion that intracapsular grafts should be fixed with the limb in a normal standing angle.A five degree of freedom test apparatus was used to evaluate the effect of graft location, graft preload, and limb flexion angle at time of graft fixation on reconstructions of the cranial cruciate ligament deficient stifle. Our results suggest that intracapsular grafts should not be fixed with the limb in 90° of flexion, but in a normal standing angle.

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