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SUMMARY:Inertial Lévy flights in bounded domains
DTSTART;VALUE=DATE-TIME:20210929T114000Z
DTEND;VALUE=DATE-TIME:20210929T120000Z
DTSTAMP;VALUE=DATE-TIME:20220809T231459Z
UID:indico-contribution-83-474@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Karol Capała (Institute of Theoretical Physics\, UJ
)\nThe escape from a given domain is one of the fundamental problems in st
atistical physics and the theory of stochastic processes. In this talk we
will explore properties of the escape of an inertial particle driven by L
évy noise from a bounded domain\, restricted by two absorbing boundaries.
The properties of the mean first passage time for the integrated Ornstein
--Uhlenbeck process driven by Lévy noise will be compared to its Brownian
counterpart i.e. randomly accelerated process. Mean first passage time co
nsiderations will be complemented by analysis of the escape velocity and e
nergy along with their sensitivity to initial conditions.\n\nhttps://zakop
ane.if.uj.edu.pl/event/17/contributions/474/
LOCATION:Online
URL:https://zakopane.if.uj.edu.pl/event/17/contributions/474/
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BEGIN:VEVENT
SUMMARY:SHOULD I STAY OR SHOULD I GO? ZERO-SIZE JUMPS IN RANDOM WALKS FOR
LÉVY FLIGHTS
DTSTART;VALUE=DATE-TIME:20210929T112000Z
DTEND;VALUE=DATE-TIME:20210929T114000Z
DTSTAMP;VALUE=DATE-TIME:20220809T231459Z
UID:indico-contribution-83-475@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Gianni Pagnini (BCAM - Basque Center for Applied Mat
hematics)\nMotivated by the fact that\, in the literature dedicated to ran
dom walks for anomalous diffusion\, it is disregarded if the walker does n
ot move in the majority of the iterations because the most frequent jump-s
ize is zero (i.e.\, the jump-size distribution is unimodal with mode locat
ed in zero) or\, in opposition\, if the walker always moves because the ju
mps with zero-size never occur (i.e.\, the jump-size distribution is bi-mo
dal and equal to zero in zero)\, we provide an example in which indeed the
shape of the jump-distribution plays a role.\nIn particular\, we show tha
t the convergence of Markovian continuous-time random walk (CTRW) models f
or Lévy flights to a density function that solves the fractional diffusio
n equation is not guaranteed when the jumps follow a bi-modal power-law di
stribution equal to zero in zero\, but\, as a matter of fact\, the resulti
ng diffusive process converges to a density function that solves a double-
order fractional diffusion equation.\nWithin this framework\, self-similar
ity is lost. The consequence of this loss of self-similarity is the emerge
nce of a time-scale for realizing the large-time limit. Such time-scale re
sults to span from zero to infinity accordingly to the power-law displayed
by the tails of the walker’s density function. Hence\, the large-time l
imit could not be reached in real systems.\nThe significance of this resul
t is two-fold: i) with regard to the probabilistic derivation of the fract
ional diffusion equation and also ii) with regard to recurrence and the re
lated concept of site fidelity in the framework of Lévy-like motion for w
ild animals.\n\nTalk based on:\nG. Pagnini and S. Vitali. Should I stay or
should I go? Zero-size jumps in random walks for Lévy flights\, Fract. C
alc. Appl. Anal.\, 24(1)\, 137–167\, 2021.\n\nhttps://zakopane.if.uj.edu
.pl/event/17/contributions/475/
LOCATION:Online
URL:https://zakopane.if.uj.edu.pl/event/17/contributions/475/
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SUMMARY:Interacting Persistent Random Walkers
DTSTART;VALUE=DATE-TIME:20210929T110000Z
DTEND;VALUE=DATE-TIME:20210929T112000Z
DTSTAMP;VALUE=DATE-TIME:20220809T231459Z
UID:indico-contribution-83-473@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Martin Evans (University of Edinburgh)\nIn this talk
I will consider persistent random walkers\, also known as run and tumble
particles\, which are emerging as a fundamental microscopic model of activ
e matter. I will review the properties of a single persistent walker then
consider the case of two persistent random walkers that interact through a
n exclusion interaction. An exact expression for the stationary state of t
wo such walkers on a periodic lattice reveals how the particles jam and ge
nerate an effective attractive potential. The full spectrum of the two-par
ticle problem can also be computed and exhibits exceptional points\, which
correspond to dynamical transitions in the relaxation time. \nJamming and
attraction of interacting run-and-tumble random walkers\, AB Slowman\, MR
Evans\, RA Blythe\, Physical review letters 116 (21)\, 218101 (2016) \nEx
act spectral solution of two interacting run-and-tumble particles on a rin
g lattice\, E Mallmin\, RA Blythe\, MR Evans\, Journal of Statistical Mech
anics: Theory and Experiment 2019 (1)\, 013204\n\nhttps://zakopane.if.uj.e
du.pl/event/17/contributions/473/
LOCATION:Online
URL:https://zakopane.if.uj.edu.pl/event/17/contributions/473/
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BEGIN:VEVENT
SUMMARY:Colossal Brownian\, yet non-Gaussian diffusion in a periodic poten
tial
DTSTART;VALUE=DATE-TIME:20210929T103000Z
DTEND;VALUE=DATE-TIME:20210929T110000Z
DTSTAMP;VALUE=DATE-TIME:20220809T231459Z
UID:indico-contribution-83-435@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Jakub Spiechowicz (University of Silesia)\nI will re
port on a novel class of Brownian\, yet non-Gaussian diffusion\, in which
the mean square displacement of the particle grows linearly with time\, th
e probability density for the particle spreading is Gaussian like\, but th
e probability distribution for its position increments possesses an expone
ntially decaying tail. In contrast to recent works in this area\, this beh
avior is not a consequence of either a space- or time-dependent diffusivit
y\, but is induced by external non-thermal noise acting on the particle dw
elling in a periodic potential. The exponential tail in the increment stat
istics leads to colossal enhancement of diffusion\, drastically surpassing
the previously researched situation known as “giant” diffusion.\n\nht
tps://zakopane.if.uj.edu.pl/event/17/contributions/435/
LOCATION:Online
URL:https://zakopane.if.uj.edu.pl/event/17/contributions/435/
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SUMMARY:Enhancing transport by shaping barriers (beating activation energi
es)
DTSTART;VALUE=DATE-TIME:20210929T100000Z
DTEND;VALUE=DATE-TIME:20210929T103000Z
DTSTAMP;VALUE=DATE-TIME:20220809T231459Z
UID:indico-contribution-83-426@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Emmanuel Trizac (Université Paris-Saclay)\nBrownian
escape is key to a wealth of physico-chemical processes\, including polym
er folding and information storage. The frequency of thermally activated e
nergy barrier crossings is assumed to generally decrease exponentially wit
h increasing barrier height. Here\, we show theoretically and experiment t
ally that higher\, fine-tuned barrier profiles result in significantly enh
anced escape rates\, in breach of the intuition relying on the above scali
ng law\, and address the corresponding conditions for maximum speed-up.\n\
nhttps://zakopane.if.uj.edu.pl/event/17/contributions/426/
LOCATION:Online
URL:https://zakopane.if.uj.edu.pl/event/17/contributions/426/
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