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Effect of very short impulses on nonlinear dissipative kinetics

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  • Fuliński, Andrzej

Abstract

Delayed nonautonomous kinetics is considered on the example of the kinetic equation Ẋ(t) = ax(t−τdel) − b(t) x2 (t−τdel), with b(t) representing a train of separate impulses. Dependence on impulse width is discussed for the case of short delay times. Sufficiently short impulses lead to significant changes in x(t): appearance of chaotic behaviour absent for longer impulses, abrupt drop of the average value of x, etc., which enables the experimental determination of τdel. It is suggested that there exists a time scale on which the “normal” macroscopic kinetic description breaks down due to the natural “inertia” of physical processes (related, e.g., to the presence of fast variables averaged out in the macroscopic description). Hence the effects described in this paper may be used for the phenomenological definition and experimental determination of a new characteristic of the macroscopic dissipative system, related to that time scale: the inertial relaxation time τinertial.

Suggested Citation

  • Fuliński, Andrzej, 1991. "Effect of very short impulses on nonlinear dissipative kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(3), pages 493-509.
    • Handle: RePEc:eee:phsmap:v:178:y:1991:i:3:p:493-509
    DOI: 10.1016/0378-4371(91)90034-A
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