· Irene Giardina ! Dept. of Physics, University of Rome La Sapienza & CNR-ISC ! CNR ! Dept. of...
Transcript of · Irene Giardina ! Dept. of Physics, University of Rome La Sapienza & CNR-ISC ! CNR ! Dept. of...
Irene Giardina!
Dept. of Physics, University of Rome La Sapienza & CNR-ISC !
CNR!
Dept. of Physics, Rome!University La Sapienza!
Institute !for Complex Systems! Accademia Nazionale dei Lincei, Rome 2017
Dynamic scaling in natural swarms
Collec3ve behaviour in biological systems
insects
mammals fish birds
bacteria cells
self-‐organized collec5ve behaviour
0
0.5
1
d eDeseigne et al, PRL 2010 Narayan et al, Science 2007 Bricard et al, Nature 2013
Analogy with sta3s3cal physics and ac3ve non-‐living ma;er
Hope: details do not ma/er – few features determine the universality class
simple models capture the large scale behavior of ac;ve ma/er
v
i(t +1) =
v
i(t) + J
v
k(t) +
ξ
i
k∈i
∑ri(t +1) =
ri(t)+vi(t +1)
vi= v
0
self-‐propelled par5cles
Vicsek model
Are these hopes/assump3ons jus3fied for animal groups
and complex biological systems?
Collec3ve behaviour in animal groups
movie by C. Carere - Starflag!
movie by S. Melillo, SWARM!
Flocks Swarms
Global order
Scale free correla;ons -‐ Collec;ve turns
Pnas 105 (2008), Pnas 107 (2010), Pnas 109 (2012)
Nature Phys 10 (2014), Jstat 2015, Nature Phys 12 (2016)
PRL 118 (2017)
Plos Comp. Biol 10 (2014) , PRL 113 (2014)
Nature Phys 13 (2017)
No global order
Correla;ons – quasi cri;cal behavior
Can we define classes of behavior ?
scaling in cri;cal phenomena
sta;c scaling
sta3c scaling hypothesis:
anomalous dimension
correla;on func;on in momentum space: control parameters
microscopic scale
correla;on length:
dynamic scaling
dynamic scaling hypothesis:
dynamical renormaliza;on group idea:
dynamic cri;cal exponent
consequences of dynamic scaling
collapse
0 60
t
0
1
C
^ (k,t
)
0 60
kzt
0
1C
^ (k
,t)
just one func;on
cri;cal slowing down
systems strongly correlated in space are also strongly correlated in ;me
scaling
renormaliza;on group
universality
universality in biological systems?
start from scaling
experiments
this is our `spin’
!i(t
0)
!j(t
0+t)
rij
c)
velocity correla;on func;on in real space and ;me
0.5t
0
1
C
^(k
,t)
k = 4.53k = 7.77k = 12.9
k = 17.5k = 23.9
dynamic correla;ons in k-‐space
natural swarms
dynamic scaling hypothesis
0 0.4t
0
1
C
^ (k,t
)
ξ = 12.7
ξ = 10.6
ξ = 8.98
ξ = 7.34
ξ = 6.06
0 8k
zt
0
1
C
^ (k,t
)
2 3logk
-2
0
log
τ k0 60
t
0
1
C
^ (k,t
)
ξ = 1.56
ξ = 1.26
ξ = 1.04
ξ = 0.85
ξ = 0.71
0 60
kzt
0
1
C
^ (k,t
)
-0.5 0 0.5
logk
2
3
4
log
τ k
z ~ 1
z ~ 2
d) e) f)
Natural Swarms
Vicsek Swarms
dynamic scaling holds and a new exponent emerges
• natural swarms:
• Vicsek swarms:
how anomalous is the exponent z = 1 ?
• Heisenberg/Ising model (Model A): z = 2
• Non-‐dissipa;ve an;ferromagnet (linear spin-‐wave) (Model G): z = 1.5
• Quantum ferromagnet (Model J): z = 2.5
• Vicsek model, ordered phase (flocks): z = 1.6
• Vicsek model, disordered phase (swarms): z = 2
equilibrium models:
ac;ve ma/er models:
such a small value of z seems to require a non-‐trivial renormaliza;on structure
scaling
renormaliza;on group
universality
non-‐dissipa;ve relaxa;on
0.20 t/k
-0.2
0
log(C
(k,t))
^
P(h
)
15
a)
b)
c)
k
15.00
x
0
0.5
1
h(x
)
Vicsek SwarmsNatural Swarms
b)
exponen;al relaxa;on -‐ dissipa;ve
non-‐exponen;al relaxa;on – non-‐dissipa;ve
t
C
^ (t)
t
C
^ (t)
t
C
^ (t)
0 0.25 0.5 0.75 10.1
x
0
1
h(x
)
deeply underdamped
underdamped
ligthly underdamped
critically damped
lightly overdamped
overdamped
deeply overdamped
effectively exponential
a) b) c)
d)
underdamped
cri;cally damped overdamped underdamped
overdamped
stochas;c harmonic oscillator
swarms
Vicsek SwarmsNatural Swarms
second-‐order iner;al dynamics ?
the system has no long-‐range order
why don’t we observe a purely dissipa;ve regime?
ξ ξL
hydrodynamic regime cri;cal regime
hydrodynamics breaks down
ξ ~ L
1 2 3
0.1
0.3
ξ
b)
L
hydrodynamic vs cri;cal regime
natural swarms
swarms are always in the
cri;cal regime
near-‐cri;cal censorship of hydrodynamics
conclusions
dynamic scaling holds in natural swarms
anomalous cri;cal exponent and non-‐dissipa;ve relaxa;on
near-‐cri;cal censorship of hydrodynamics
arXiv:1611.08201
Nature Physics, 06/2017
Andrea Cavagna
Alessandro AVanasi
Lorenzo Del Castello
Agnese d’Orazio
Asja Jelic
Stefania Melillo
Leonardo Parisi
Oliver Pohl
Edward Shen
Edmondo Silvestri
Massimiliano Viale
Tomas Grigera
COBBS Group – Collec;ve Behaviour in Biological Systems
Daniele Con5