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Phase space structure and dynamics for the Hamiltonian isokinetic thermostat
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10.1063/1.3455712
/content/aip/journal/jcp/133/1/10.1063/1.3455712
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/1/10.1063/1.3455712

Figures

Image of FIG. 1.
FIG. 1.

(a) Section through the physical potential , Eq. (19), , , . (b) Section through the exponentiated potential, , .

Image of FIG. 2.
FIG. 2.

Lifetime distributions for the three DOF Hamiltonian isokinetic thermostat. The lifetime distribution is derived from the distribution of gap times obtained by initiating trajectories on the incoming DS and propagating them until they cross the outgoing DS. (a) H121, . (b) H321, . (c) H521, .

Image of FIG. 3.
FIG. 3.

Coordinate distributions for three DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) H121, . (b) H321, . (c) H521, .

Image of FIG. 4.
FIG. 4.

Coordinate distributions for three DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) H121, . (b) H321, . (c) H521, .

Image of FIG. 5.
FIG. 5.

Coordinate distributions for three DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) H121, . (b) H321, . (c) H521, .

Image of FIG. 6.
FIG. 6.

Moments of the distribution of the coordinate obtained using the three DOF Hamiltonian isokinetic thermostat (squares) are compared with those for the Boltzmann distribution (circles). Odd moments for the Boltzmann distribution are identically zero. (a) H121, . (b) H321, . (c) H521, .

Image of FIG. 7.
FIG. 7.

Lifetime distributions for the four DOF Hamiltonian isokinetic thermostat. The lifetime distribution is derived from the distribution of gap times obtained by initiating trajectories on the incoming DS and propagating them until they cross the outgoing DS. (a) J121, . (b) J321, . (c) J521, .

Image of FIG. 8.
FIG. 8.

Coordinate distributions for four DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) J121, . (b) J321, . (c) J521, .

Image of FIG. 9.
FIG. 9.

Coordinate distributions for four DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) J121, . (b) J321, . (c) J521, .

Image of FIG. 10.
FIG. 10.

Moments of the distribution of the coordinate obtained using the four DOF Hamiltonian isokinetic thermostat (squares) are compared with those for the Boltzmann distribution (circles). Odd moments for the Boltzmann distribution are identically zero. (a) J121, . (b) J321, . (c) J521, .

Image of FIG. 11.
FIG. 11.

Comparison of the numerically determined for the four DOF harmonic potential with the theoretical expression (A14) over the energy range . The phase space volume was determined by random sampling of a phase space hypercube using points. All are divided by [cf. Eq. (A15)].

Image of FIG. 12.
FIG. 12.

Number of points per energy bin vs energy (width , ) for the J321 four DOF Hamiltonian. The red curve is a fit to the numerical data using a fifth-order polynomial. The fit to the data yields a value .

Tables

Generic image for table
Table I.

Computed mean gap times, fluxes, reactive phase space volumes, energy surface volumes, and entropy deficits for lifetime distributions for three DOF and four DOF model Hamiltonians. Details of the computations are discussed in Appendix B.

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/content/aip/journal/jcp/133/1/10.1063/1.3455712
2010-07-07
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Phase space structure and dynamics for the Hamiltonian isokinetic thermostat
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/1/10.1063/1.3455712
10.1063/1.3455712
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