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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Phase transitions in persistent and run-and-tumble
walks - Raúl Toral (Universitat de les Illes Bale
ars)
DTSTART;TZID=Europe/London:20231106T100000
DTEND;TZID=Europe/London:20231106T110000
UID:TALK203194AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/203194
DESCRIPTION:The motion of active matter\, like bacteria and ot
her tiny particles\, has been studied extensively
using mathematical models such as persistent and r
un-and-tumble random walks. These models incorpora
te a memory element\, making it more likely for th
e walker to move in the same direction as their pr
evious step. In this talk\, I will explore various
random-walk models\, with a specific focus on cal
culating the large-deviation function. This functi
on helps us understand how the end-to-end distance
scales with the number of steps taken. Additional
ly\, I will consider its Laplace transform\, the s
o-called Langevin function providing insight into
the relationship between force and extension. When
persistence is present\, there are some unexpecte
d phenomena that are absent in walks without memor
y. Firstly\, in on-lattice random walks with persi
stence in spatial dimension three or larger\, two
new inflexion points appear in the Langevin functi
on. This suggests an initial softening phase befor
e the usual stiffening\, which occurs beyond a cri
tical force level. For off-lattice random walks wi
th persistence and run-and-tumble walks in spatial
dimension larger than four\, the large deviation
function undergoes a first-order phase transition.
In the corresponding force-versus-extension relat
ion\, this transition manifests as the attainment
of complete extension at a finite force magnitude.
Analytically\, the origin of this phenomenology b
ears many similarities with the calculation of the
partition function of an ideal quantum boson gas\
, and the phase transitions found have the same ma
thematical origin than the Bose-Einstein condensat
ion.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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