This work focuses on the dynamics of a ball inside the reactor of a ball mill. We show that the distribution of collisions at the reactor walls exhibits multifractal properties in a wide region of the parameter space defining the geometrical characteristics of the reactor and the collision elasticity. This feature points to the presence of restricted self-organized zones of the reactor walls where the ball preferentially collides and the mechanical energy is mainly dissipated.

1.
S. L.
James
,
C. J.
Adams
 et al,
Chem. Soc. Rev.
41
,
413
447
(
2012
).
2.
F.
Delogu
,
G.
Mulas
,
M.
Monagheddu
,
L.
Schiffini
, and
G.
Cocco
,
Int. J. Non-Equilib. Process.
11
,
235
(
1998
).
3.
A.
Concas
,
N.
Lai
,
M.
Pisu
, and
G.
Cao
,
Chem. Eng. Sci.
61
,
3746
3760
(
2006
).
4.
R.
Watanabe
,
H.
Hashimoto
, and
G.
Geun Lee
,
Mater. Trans., JIM
36
(
2
),
102
(
1995
).
5.
S.
Budin
,
I.
Putra Almanar
,
S.
Kamaruddin
 et al,
J. Mater. Process. Technol.
209
,
4312
4319
(
2009
).
6.
F.
Delogu
,
M.
Monagheddu
,
G.
Mulas
,
L.
Schiffini
, and
G.
Cocco
,
Int. J. Non-Equilib. Process.
11
,
235
(
2000
).
7.
M.
Rustici
,
G.
Mulas
, and
G.
Cocco
,
Mater. Sci. Forum
225–227
,
243
(
1996
).
8.
G.
Heinicke
,
Tribochemistry
(
Akademie Verlag
,
Berlin
,
1984
).
9.
E. M.
Gutman
,
Mechanochemistry of Materials
(
Cambridge International Science Publishing
,
Cambridge
,
1998
).
10.
V. I.
Levitas
, in
High Pressure Surface Science and Engineering
, edited by
Y.
Gogotsi
and
V.
Domnich
(
Institute of Physics
,
Bristol
,
2004
), Chap. 3, p.
159
.
11.
P.
Balaz
,
Mechanochemistry in Nanoscience and Minerals Engineering
(
Springer-Verlag
,
Berlin
,
2008
).
12.
M. K.
Beyer
and
H.
Clausen-Schaumann
,
Chem. Rev.
105
,
2921
(
2005
).
13.
B.
Rodriguez
,
A.
Bruckmann
,
T.
Rantanen
, and
C.
Bolm
,
Adv. Synth. Catal.
349
,
2213
(
2007
).
14.
M. M.
Caruso
,
D. A.
Davis
,
Q.
Shen
,
S. A.
Odom
,
N. R.
Sottos
,
S. R.
White
, and
J. S.
Moore
,
Chem. Rev.
109
,
5755
(
2009
).
15.
Experimental and Theoretical Studies in Modern Mechanochemistry
, edited by
F.
Delogu
and
G.
Mulas
(
Transworld Research Network
,
Trivandrum, Kerala
,
2010
).
16.
High-Energy Ball Milling
, edited by
M.
Sopicka-Lizer
(
Woodhead Publishing
,
London
,
2010
).
17.
L.
Takacs
,
Chem. Soc. Rev.
42
,
7649
7659
(
2013
).
18.
P.
Balaz
,
M.
Achimovicova
,
M.
Balaz
,
P.
Billik
,
Z.
Cherkezova-Zheleva
,
J. M.
Criado
,
F.
Delogu
,
E.
Dutkova
,
E.
Gaffet
,
F. J.
Gotor
,
R.
Kumar
,
I.
Mitov
,
T.
Rojac
,
M.
Senna
,
A.
Streletskii
, and
K.
Wieczorek-Ciurowa
,
Chem. Soc. Rev.
42
,
7571
(
2013
).
19.
C.
Caravati
,
F.
Delogu
,
G.
Cocco
, and
M.
Rustici
,
Chaos
9
(
1
),
219
(
1999
).
20.
G.
Manai
,
F.
Delogu
, and
M.
Rustici
,
Chaos
12
,
601
609
(
2002
).
21.
V.
Petrov
,
V.
Gáspár
,
J.
Masere
, and
K.
Showalter
,
Nature
361
,
240
(
1993
).
22.
P.
Grassberger
and
I.
Procaccia
,
Phys. Rev. Lett.
50
,
346
349
(
1983
).
23.
P.
Grassberger
and
I.
Procaccia
,
Physica D
9
,
189
208
(
1983
).
24.
P.
Grassberger
,
Phys. Lett. A
148
,
63
68
(
1990
).
25.
J.
Theiler
,
J. Opt. Soc. Am. A
7
,
1055
1073
(
1990
).
26.
H.
Kantz
and
T.
Schreiber
,
Nonlinear Time Series Analysis
(
Cambridge University Press
,
Cambridge
,
1997
).
27.
T. C.
Halsey
,
M. H.
Jensen
,
L. P.
Kadanoff
,
I.
Procaccia
, and
B. I.
Shraiman
,
Phys. Rev. A
33
,
1141
1151
(
1986
).
28.
H. G. E.
Hentschel
and
I.
Procaccia
,
Physica D
8
,
435
444
(
1983
).
29.
E.
Ott
,
Chaos in Dynamical Systems
(
Cambridge University Press
,
2002
).
30.
S. H.
Strogatz
,
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
(
Westview Press
,
1994
).
31.
P. C.
Ivanov
 et al,
Nature (London)
399
,
461
(
1999
).
32.
D.
Pastén
,
V.
Munoz
,
A.
Cisternas
,
J.
Rogan
, and
J. A.
Valdivia
,
Phys. Rev. E
84
,
066123
(
2011
).
33.
K.-A.
Liu
and
L.
I
,
Phys. Rev. E
86
,
011924
(
2012
).
34.
U.
Frisch
,
Turbulence
(
Cambridge University Press
,
New York
,
1995
).
35.
K. P.
Zybin
and
V. A.
Sirota
,
Phys. Rev. E
88
,
043017
(
2013
).
36.
J.
Perelló
,
J.
Masoliver
,
A.
Kasprzak
, and
R.
Kutner
,
Phys. Rev. E
78
,
036108
(
2008
).
37.
G. Z.
dos Santos Lima
,
M. A.
Correa
,
R. L.
Sommer
, and
F.
Bohn
,
Phys. Rev. E
86
,
066117
(
2012
).
38.
M. A.
Budroni
,
M.
Rustici
, and
E.
Tiezzi
,
Physica A
389
,
3883
3891
(
2010
).
39.
E. H.
Love
,
A Treatise on the Mathematical Theory of Elasticity
, 4th ed. (
Dover
,
New York
,
1944
).
40.
S. P.
Timoshenko
and
J. N.
Goodier
,
Theory of Elasticity
(
McGraw-Hill
,
New York
,
1970
).
41.
The ball dynamics inside a cylindrical reactor where the oscillatory mode on the equatorial plane is frozen strictly lies on the vertical intersection plane localized by the initial position of the milling body.
42.
R. H.
Riedi
,
J. Math. Anal. Appl.
189
,
462
(
1995
).
43.
R.
Pastor-Satorras
and
R. H.
Riedi
,
J. Phys. A: Math. Gen.
29
,
391
(
1996
).
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