The Fermi–Pustyl'nikov model, named after

Enrico Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and ...

and Lev Pustyl'nikov, is a model of the Fermi acceleration mechanism. A point mass falls with a constant

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

vertically on the infinitely heavy horizontal wall, which moves vertically in accordance with analytic periodic law in time. The point interacts with the wall by the law of

elastic collision In physics, an elastic collision is an encounter (collision) between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into o ...

. For this model it was proved that under some general conditions the

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

and

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

of the point at the moments of collisions with the wall tend to infinity for an

open set In mathematics, open sets are a generalization of open intervals in the real line. In a metric space (a set along with a distance defined between any two points), open sets are the sets that, with every point , contain all points that are suf ...

of initial data having the infinite

Lebesgue measure In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of ''n''-dimensional Euclidean space. For ''n'' = 1, 2, or 3, it coincides wit ...

.L. D. Pustyl'nikov (1977), Stable and oscillating motions in nonatonomous dynamical systems II. (Russian) Trudy Moscow. Mat. Obsc. 34, 3–103. English transl. in ''Trans. Moscow Math. Soc. (2), (1978). This model was introduced in 1968 in,L. D. Pustyl'nikov (1968), On a dynamical system. (Russian) Uspekhi Mat. Nauk 23, no. 4 (142), 251-252. and studied in, by L. D. Pustyl'nikov in connection with the justification of the Fermi acceleration mechanism. (See also L. D. Pustyl'nikov (1995), Poincaré models, rigorous justification of the second law of thermodynamics from mechanics, and Fermi acceleration mechanism. ''Russ. Math. Surveys'' 50(1), 145–189. and references therein).

References

Dynamical systems {{Systemstheory-stub