Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling of the dynamical properties of the Fermi-Ulam accelerator model   The chaotic sea below the lowest energy spanning curve of the complete
Fermi-Ulam model (FUM) is numerically investigated when the amplitude of
oscillation 'epsilon' of the moving wall is small. We use scaling analysis near
the integrable to non-integrable transition to describe the average energy as
function of time t and as function of iteration (or collision) number n. If t
is employed as independent variable, the exponents related to the energy
scaling properties of the FUM are different from the ones of a well known
simplification of this model (SFUM). However, if n is employed as independent
variable, the exponents are the same for both FUM and SFUM. In the collision
number analysis, we present analytical arguments supporting that the exponents
c* and b* related to the initial velocity and to 'epsilon' are given by c* =
-1/2 and b* = -1. We derive also a relation connecting the scaling exponents
related to the variables time and collision number. Moreover, we show that,
differently from the SFUM, the average energy in the FUM saturates for long
times and we justify the physical origins for some differences and similarities
observed between the FUM and its simplification.

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The categories of this paper are: physics
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math