Periodic orbit expansions for the Lorentz gas

1994 ◽  
Vol 75 (3-4) ◽  
pp. 553-584 ◽  
Author(s):  
Gary P. Morris ◽  
Lamberto Rondoni
Keyword(s):  
Periodic Orbit ◽  
Lorentz Gas

scholarly journals Chaos and Its Impact on the Foundations of Statistical Mechanics

1996 ◽  
Vol 49 (1) ◽  
pp. 51 ◽  
Author(s):  
Gary P Morriss ◽  
Lamberto Rondoni
Keyword(s):  
Periodic Orbit ◽  
Lorentz Gas ◽  
Analytic Formula ◽  
Numerical Techniques ◽  
Lyapunov Numbers ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
Definition Of ◽  
Dynamics Simulations ◽  
Good Agreement

In this work we present a brief derivation of the periodic orbit expansion for simple dynamical systems, and then we apply it to the study of a classical statistical mechanical model, the Lorentz gas, both at equilibrium and in a nonequilibrium steady state. The results are compared with those obtained through standard molecular dynamics simulations, and they are found to be in good agreement. The form of the average using the periodic orbit expansion suggests the definition of a new dynamical partition function, which we test numerically. An analytic formula is obtained for the Lyapunov numbers of periodic orbits for the nonequilibrium Lorentz gas. Using this formula and other numerical techniques we study the nonequilibrium Lorentz gas as a dynamical system and obtain an estimate of the upper bound on the external field for which the system remains ergodic.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Hard Ball Systems and the Lorentz Gas

2000 ◽  
Author(s):  
L. A. Bunimovich ◽  
D. Burago ◽  
N. Chernov ◽  
E. G. D. Cohen ◽  
C. P. Dettmann ◽  
...  
Keyword(s):  
Lorentz Gas ◽  
Hard Ball

Periodic orbit expansions for classical smooth flows

1991 ◽  
Vol 24 (5) ◽  
pp. L237-L241 ◽  
Author(s):  
P Cvitanovic ◽  
B Eckhardt
Keyword(s):  
Periodic Orbit
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