Fractals
in Physics| Fractals
in Physics |
In General
* History: 1915, J
Perrin, Brownian motion and snowflakes; 1972, K Wilson, Scale invariance
in phase transitions and renormalization group; 1980s, Cosmology,
diffusion-limited
aggregation, dielectric breakdown.
* Kinematical description:
Fractal geometry; Notice that physical fractals are usually random.
* Models for fractal growth:
Ising model; Dielectric breakdown; Critical percolation clusters.
* Goals: Develop new
concepts, related to self-organization, irreversibility and non-ergodicity,
to understand the origin of fractal structure.
* Applications: Aggregation;
Diffusion; Percolation; Chaotic dynamics [coordinate-independent indicator].
@ General references: Amann et al ed-88; Pietronero PRP(89)
[growth]; Hurd AJP(88)nov-RL;
Gouyet 96; Addison 97; Aguirre et al RMP(09) [fractal basins in non-linear
dynamics].
@ And quantum mechanics: Cannata & Ferrari AJP(88)aug
[particle paths]; issue CSF(94)#3;
Kröger
PRP(00);
Wójcik et al PRL(00)qp [fractal
wave functions].
@ Random fractal networks: Nakayama et al RMP(94)
[dynamics and scaling].
@ Related topics: Porter gq/02 ['fractafolds'
as spacetime structure]; Ishikawa & Suzuki
PhyA(04)
[breaking of fractal distribution]; Liaw & Chiu PhyA(09) [fractal dimension
of
a time sequence].
> Related topics: see electromagnetic
fields; phase
transitions; stochastic
processes; thermodynamical systems;
turbulence.
Gravitation and Cosmology > s.a. cosmology; quantum
spacetime.
* Fractal spacetime:
One motivation is obtaining a discrete spacetime that is invariant under the
renormalization
group.
* Galaxy distribution:
A fractal structure in the distribution of luminous matter up to about 5–15
Mpc has been seen and is accepted by most of the community; 1995, L Pietronero
and collaborators have been claiming for years that at all observed
scales
the pattern continues, and that there is no
evidence
of homogeneity at any scale; Although Pietronero et al seem to have done
the best
analysis of the galaxy distribution, there would remain the puzzle
of
why the cosmic microwave background is so isotropic, and the dark matter
distribution
is unknown; 2004, The consensus is that the distribution does become homogeneous
above 100 Mpc or so.
* Inside the Milky Way:
There is some evidence that the interstellar matter in our galaxy is fractally
distributed
as well.
@ Galaxy distribution: Ribeiro in(94)-a0910; Sylos
Labini et al ap/97-in,
PRP(98)ap/97,
ap/98;
Gabrielli et al EPL(99)ap/98 [gravitational
force]; Terazawa MPLA(98);
Combes ap/99-in;
Pietronero & Sylos
Labini ap/99-in, ap/00-in;
Baryshev ap/99-in
[rev]; McCauley Frac(98)ap/00;
Ribeiro GRG(01)ap;
Baryshev & Teerikorpi
02 [I].
@ Fractal spacetime: Crane & Smolin NPB(86);
Englert FP(87);
Svozil JPA(87)
[quantum field theory and regularization]; Nottale IJMPA(89),
93, CSF(94);
Ambjørn & Watabiki NPB(95)ht [dimension
from
2-point
function];
Kobelev ht/00 [multifractal];
Castro et al ht/00 [?];
Castro CSF(01)ht/00 [and
non-commutative
geometry]; Lauscher & Reuter JHEP(05)
[in asymptotically safe gravity]; Agop & Gottlieb JMP(06)
[gravity]; > s.a. quantum groups.
@ Fractal spacetime, consequences: Hill PRD(03)ht/02;
Iovane CSF(04)ap/03 [G(t), a··];
Shapovalova G&C(03)
[metric fluctuations]; Goldfain CSF(04)
[and gauge hierarchy
problem], CSF(05)
[and unified field theory].
Other Areas > s.a. random
walk.
* Examples: Crystal growth, forest fires, fibrillations.
@ Geology / geophysics: Turcotte 92 [r PT(93)may];
issue CSF(04)#2.
@ Physiology: Bassingthwaighte et al 94; West & Deering PRP(94);
Brú
et al PRL(98)
[tumor growth].
@ Related topics: Falkenberg & Namuth 98 [art, Pollock, pw(99)oct].
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send feedback and suggestions to bombelli at olemiss.edu – modified 26
oct 2009