ETTORE MAJORANA FOUNDATION AND CENTRE FOR...
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Page | 1 ETTORE MAJORANA FOUNDATION AND CENTRE FOR SCIENTIFIC CULTURE TO PAY A PERMANET TRIBUTE TO GALILEO GALILEI, FOUNDER OF MODERN SCIENCE AND TO ENRICO FERMI, "THE ITALIAN NAVIGATOR", FATHER OF THE WEAK FORCES INTERNATIONAL SCHOOL OF STATISTICAL PHYSICS (Peter Hänggi, Fabio Marchesoni, Directors) COURSE III Single file dynamics in biophysics & related areas & extensions in higher dimensions Directors: Ophir Flomenbom, Alessandro Taloni. Organizing committee: Francois Peeters, Cécile Fradin, Luciano Moffatt, Misko Vyacheslav, Ramón Castañeda-Priego. July 4-9, 2014 ETTORE MAJORANA CENTRE Via Guarnotta, 26 91016 ERICE (Sicily) - Italy Tel: +39-923-869133 Fax: +39-923-869226
Transcript of ETTORE MAJORANA FOUNDATION AND CENTRE FOR...
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ETTORE MAJORANA FOUNDATION AND CENTRE FOR
SCIENTIFIC CULTURE
TO PAY A PERMANET TRIBUTE TO GALILEO GALILEI, FOUNDER OF MODERN SCIENCE
AND TO ENRICO FERMI, "THE ITALIAN NAVIGATOR", FATHER OF THE WEAK FORCES
INTERNATIONAL SCHOOL OF STATISTICAL PHYSICS
(Peter Hänggi, Fabio Marchesoni, Directors)
COURSE III
Single file dynamics in biophysics & related areas & extensions in higher dimensions
Directors: Ophir Flomenbom, Alessandro Taloni.
Organizing committee: Francois Peeters, Cécile Fradin, Luciano
Moffatt, Misko Vyacheslav, Ramón Castañeda-Priego.
July 4-9, 2014
ETTORE MAJORANA CENTRE
Via Guarnotta, 26
91016 ERICE (Sicily) - Italy
Tel: +39-923-869133
Fax: +39-923-869226
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SPONSORS
http://www.onr.navy.mil/en/Science-Technology/ONR-Global.aspx
EMCSC - E. Majorana Centre for Scientific Culture
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PROGRAM
9:00am through 12:55pm Lunch 3:25pm through 6:55pm dinner
FRI 4th
arrival day
gathering
9:25pm
SAT 5th Fabio Marchesoni 15min
Alessandro Taloni 55min
coffee break 30 min
Ophir Flomenbom 45min
Eli Barkai 55min
Henk van Beijeren 45min
Deepak Kumar 45min
coffee break, 30min
Takeshi Ooshida 45min
poster session
SUN 6th Francois Peeters 25min
Misko Vyacheslav 55min
coffee break 35 min,
including conference photo
Paul Leiderer 55min
David Rees 45min
Cristophe Coste 45min
Artem Ryabov 45min
coffee break 30min
Michael Lomholt 45min
Unique session
conference
dinner
MON 7th Remigijus Lape 45 min
John E Pearson 45 min
Luciano Moffatt 45min
coffee break 30 min
Bert de Groot 45 min
Lorin Milescu 45 min
Ophir Flomenbom, 25 min
Cécile Fradin, 55 min
John E Pearson, 25 min
coffee break 30min
Thomas Franosch, 55 min
TUE 8th Jörg Kärger 55 min
Pino Suffritti 45 min
coffee break
Karolis Misiunas 45 min
Kwinten Nelissen 45 min
excursion & dinner
WED 9th
departure day
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TIME TABLE
Comment: the lectures’ durations in the plan include the 5 minute question duration per lecture & the
organizational time among lectures.
Day 1: Friday, July4th.
Arrival
9:25pm: Gathering in the wine cellar at the Majorana Centre, meeting with the
organizers, informal.
Day 2: Saturday, July 5th.
Session 1: basic & advanced results in single file dynamics, & biophysical
processes’ relation.
9:00: Fabio Marchesoni (University of Camerino): Opening statements of the
Program Directors.
9:15 – 10:15: Alessandro Taloni (CNR-IENI): Interacting single file systems: A
single particle approach.
10:15 – 10: 45: coffee break.
10:45 – 11:35: Ophir Flomenbom (Flomenbom-BPS Ltd): Advanced properties in
Single File Dynamics.
11:35 – 12:35: Eli Barkai (Bar Ilan University): Everlasting effect of initial
conditions on single-file diffusion.
lunch
Session 2: unique statistical & mathematical relations in files, expanding files
& extensions.
3:25 – 4:10: Henk van Beijeren (Utrecht University): On the tight connection
between collective and tagged particle motion in single file dynamics
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4:10 –4:55: Deepk Kumar (Jawaharlal Nehru University): Correlations in single
file diffusion: Open and closed systems
4:55 – 5:25: coffee break
5:25 – 6:15: Takeshi Oshida (Tottori University): Collective motion in dense
colloidal suspensions calculatedwith a two-dimensional version of the Alexander-
Pincus formula in a convected coordinate system.
6:15 – 7:05: Poster session: Anna Vasylenko (Universiteit Antwerpen), Tommy
Dessup (CNRS), Lucena Diego (Federal University of Ceará), Kwinten Nelissen
(Universiteit Antwerpen), Gajda Janusz (Wroclaw University of Technology),
Karolis Misiunas (University of Cambridge).
Day 3: Sunday, July 6th.
Session 3: single files in physics and materials science.
9:00 – 9:25: François Peeters (Universiteit Antwerpen): Introduction: Files in
physics.
9:25 – 10:25: Vyacheslav Misko (Universiteit Antwerpen): Single-file dynamics of
interacting particles in confined systems.
10:25 – 11:00: coffee break & conference photo.
11:00–12:00: Paul Leiderer (Universitat Konstanz): Transport of surface state
electrons on liquid helium through narrow channels.
12:00–12:45: David Rees (National Chiao Tung University): Single file transport
of classical electrons on the surface of liquid helium.
lunch
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Session 4: advanced properties in files.
3:25 – 4:15: Cristophe Coste (CNRS): Longitudinal and transverse single file
diffusion in quasi-1D systems.
4:15 – 5:05, Artem Ryabov (Charles University in Prague): Single-file system with
absorbing boundary: Tracer dynamics and first-passage properties.
5:05 – 5:35, coffee break
5:35– 6:25, Michael Lomholt (University of Southern Denmark): Universality and
non-universality of mobility in heterogeneous single-file systems.
6:25 – 7:05: oral communications: Gajda Janusz (Wroclaw University of
Technology); Lucena Diego (Federal University of Ceará), perhaps others.
8:15, conference unique dinner
Day 4: Monday, July 7th.
Session 5: files in biological channels.
9:00 – 9:45: Remigijus Lape (University College London): On the activation
mechanism of pentameric ligand-gated ion channels.
9:45 – 10:30: John E Pearson (Los Alamos National Laboratory): A Data-Driven Approach to Constructing a Kinetics Model of the IP3 Receptor/Ca2+ Channel in SF9 Cells. 10:30 – 11:15, Luciano Moffatt (University of Buenos Aires): Kinetic information
out of macroscopic fluctuations,
11:15 – 11:45: coffee break.
11:45 through 12:30: Bert de Groot (Max Planck Institute for Biophysical
Chemistry): The molecular dynamics of single file ion and water permeation.
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12:30– 1:15: Lorin Milescu (University of Missouri): From single molecules to
cells: testing ion channel models in live neurons.
lunch
Session 6: files in higher dimensional biological systems.
3:25–3:55: Ophir Flomenbom (Flomenbom-BPS Ltd): Slow files in 1D & higher
dimensions.
3:55 –4:55: Cécile Fradin (McMaster University): Setting apart anomalous from
simple diffusion - and everything in between – utilizing variable length-scale
measurements.
4:55 –5:25: John E Pearson (Los Alamos National Laboratory): Messages Do
Diffuse Faster than Messengers: Reconciling Disparate Estimates of the
Morphogen Bicoid Diffusion Coefficient.
5:25 – 5:55, coffee break
5:55 – 6:55: Thomas Franosch (University of Innsbruck): Rounding of the
localization transition in model crowded media.
dinner
Day 5: Tuesday, July 8th
Session 7: files in channels in physics & chemistry.
9:00 – 10:00: Jörg Kärger (Universitat Leipzig): Experimental evidence of single-
file constraints in nanoporous host-guest systems: Mysteries of guest diffusion in
the channel network of zeolites.
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10:00 – 10:50: Pino Suffritti (Universitá di Sassari): Problems in modelling single
file diffusion of water adsorbed in zeolites: computer simulations and
comparison with recent theory.
10:50 – 11:20, coffee break
11:20 – 12:10: Kwinten Nelissen (Universiteit Antwerpen), Diffusion of
Interacting Particles in Discrete Geometries.
12:10– 12:55: Karolis Misiunas (University of Cambridge), Optimizing diffusive
transport through a synthetic membrane channel.
Lunch
2:15, Session 8: excursion & dinner (further information at the place).
Day 6: Wednesday, July 9th
departure
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PARTICIPANTS, COMMUNICATORS & CONTRIBUTORS
*1* Ophir Flomenbom,
Flomenbom-BPS Ltd
19 Louis Marshal St., Tel Aviv
Israel 62668
*4* Fabio Marchesoni,
Università di Camerino, Piazza
Cavour 19/f 62032 Camerino,
Italy,
& INFN, Via A. Pascoli, I-06123
Perugia, Italy,
*7* Francois Peeters,
Universiteit Antwerpen,
Prinsstraat 13, 2000 Antwerpen,
BELGUIM,
*10* Taloni Alessandro,
CNR-IENI,
Via R. Cozzi 53, 20125 Milano,
Italy
*13* C Coste,
CNRS, Centre national de la
recherche scientifique 3, rue
Michel-Ange 75794 Paris cedex
16, France
christophe.coste@univ-paris-
diderot.fr
*16* Thomas Franosch,
University of Innsbruck, Innrain
52, A-6020 Innsbruck, Austria
*19* Artem Ryabov
Charles University in Prague,
Ovocný trh 3-5, 116 36 Praha 1
Czech Republic
*2* Cécile Fradin,
McMaster University,
1280 Main Street West |
Hamilton, Ontario L8S4L8
Canada,
*5* Luciano Moffatt,
Universidad de Buenos Aires,
Viamonte 430/44 st., Buenos
Aires, Argentina
*8* BERT de Groot,
Max Planck Institute for
Biophysical Chemistry,
Am Faßberg 11, 37077 Göttingen,
Germany,
*11* David Rees,
NCTU-RIKEN Joint Research
Laboratory, Institute of Physics,
National Chiao Tung University,
1001 University Road, Hsinchu,
Taiwan 300, ROC
& Riken, 2-1 Hirosawa, Wako,
Saitama 351-0198, Japan,
*14* Vyacheslav Misko,
Universiteit Antwerpen,
Prinsstraat 13, 2000 Antwerpen,
BELGUIM,
*17* Tommy Dessup,
CNRS, Centre national de la
recherche scientifique 3, rue
Michel-Ange 75794 Paris cedex
16, France
*20* Takeshi Ooshida,
Tottori University, JP-680-8552,
*3* Deepak Kumar,
Jawaharlal Nehru University,
New Mehrauli Road, New
Delhi 110067, India
*6* Jörg Kärger,
Universitat Leipzig,
Augustusplatz 10, 04109
Leipzig, Germany
leipzig.de
*9* Eli barkai,
Bar Ilan University,
Ramat Gan 52900
Israel,
*12* John E Pearson,
Los Alamos National
Laboratory, Casa Grande Dr,
Santa Fe National Forest, Los
Alamos National Laboratory
Los Alamos, NM 87544
USA,
*15* Henk van BEIJEREN,
Utrecht University, Domplein
29, 3512 JE Utrecht, The
Netherlands,
*18* Pino Suffritti,
University of Sassari, Piazza
D'Armi, 17, 07100 Sassari,
Italy:
*21* Lorin Milescu,
University of Missouri,
Columbia, MO 65211, USA
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*22* Anna Vasylenko,
Universiteit Antwerpen,
Prinsstraat 13, 2000 Antwerpen,
BELGUIM,
*25* Kwinten Nelissen,
Universiteit Antwerpen,
Prinsstraat 13, 2000 Antwerpen,
BELGUIM,
*28* Paul Leiderer, Universität Konstanz
78457 Konstanz, Germany [email protected]
*31* Posch Harald,
University of Vienna
Boltzmanngasse 5
A-1090 Wien, Austria
*34* Peter Hanggi
Institut f. Physik, Universitaet
Augsburg, Universitätsstraße 2,
86135 Augsburg, Germany
*37* Alessandra Cambi,
Nijmegen Centre for Molecular
Life Sciences, 259 RIMLS
P.O. Box 9101, 6500 HB Nijmegen
The Netherlands
*40* Paul Higgs,
McMaster university,
1280 Main St W, Hamilton, ON L8S
4L8, Canada
Tottori, Japan
*23* Michael Lomholt,
University of Southern Denmark,
Campusvej 55, 5230 Odense M,
Denmark,
*26* Stanislav Kozubek,
Masaryk University
Kamenice 126/3, 625 00
Brno, Czech Rebuplic
*29* Janusz Gajda,
Wroclaw University of
Technology, 27 Wybrzeże
Wyspiańskiego St 50-370
Wrocław, Poland
*32* Ramón Castañeda-Priego,
Physical Engineering Department,
University of Guanajuato,
Lascuráin de Retana No. 5
Guanajuato, Gto., México Col.
Centro C.P. 36000, Mexico
*35* Karolis Misiunas,
University of Cambridge, Cavendish Laboratory, 19 JJ Thomson
Ave, Cambridge CB3, United
Kingdom
*38* A. P. Philipse,
University of Utrecht University,
Domplein 29, 3512 JE Utrecht,
The Netherlands,
*41* Wim Wenseleers
Universiteit Antwerpen,
Prinsstraat 13, 2000 Antwerpen,
BELGUIM,
*24* Diego Lucena,
Universidade Federal do
Ceará, Rua Coronel
Estanislau Frota - Centro,
Fortaleza-CE, 62010-560,
Brazil
*27* Remigijus Lape,
University College London,
Gower St, London WC1E
6BT,
UNITED KINGDOM
*30* Elchin Huseynov,
Instiute of Radiation
Problems of Azerbaijan
National Academy of
Sciences, AZ 1143,
B.Vahabzadeh 9, Baku,
Azerbaijan,
*33* Michel Saint Jean,
CNRS, Centre national de la
recherche scientifique 3, rue
Michel-Ange 75794 Paris
cedex 16, France
michel.saint-
*36* Ralf Metzler
University of Potsdam,
Am Neuen Palais 10, 14469
Potsdam, Germany
*39* Larysa baraban,
Dresden University of
Technology,
Mommsenstraße 11, 01069
Dresden, Germany
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*42* Edith Cristina Euán-Díaz
Universiteit Antwerpen,
Prinsstraat 13, 2000 Antwerpen,
BELGUIM,
*43* Dario Villamaina
Laboratoire de Physique
Théorique
École Normale Supérieure
24 rue Lhomond
75231 Paris Cedex 05
France
*44* Piero Sozzani,
University of Milan Bicocca
20125 Milano, Italy
*** family members’ attendance: 5 family members from 3 families. *** 33 Participants in the Majorana Centre, 2 arrange accommodation.
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ABSTRACTS
*1* Ophir Flomenbom, Flomenbom-BPS, Ltd
Advanced properties in Single File Dynamics
&: Slow files in 1d & higher dimensions
The basic single file process is the diffusion of N (N → ∞) identical Brownian hard spheres in a
quasi-one-dimensional channel of length L (L → ∞), such that the spheres remain ordered, and the
average particle's density is approximately fixed. The most known statistical properties in this process
are that the mean square displacement (MSD) of a particle in the file follows, MSD~t1/2 and
its probability density function (PDF) is a Gaussian in position with a variance, MSD.
I’LL focus in first talk on the following matters [1, 2, 3, 4]:
(1) First, the question about the origin of the unique scaling, MSD~t1/2, in simple files, is answered with
scaling law analysis and a new approach for full mathematical computations in normal files.
(2) The MSD is derived in normal files with particles’ density that is not fixed and with particles that
are not identical, yet, the diffusion coefficients of the particles are distributed according to a
probability density function. Results in these files follow:
In files with a density law that is not fixed, but decreases as a power law with an exponent a with
the distance from the origin, the particle in the origin MSD scales like, MSD~t[1+a]/2, with a
Gaussian PDF [1].
When, in addition, the particles' diffusion coefficients are distributed like a power law with
exponent γ (around the origin), the MSD follows, MSD~tμ, where, μ = [1-γ] / [2/(1+a) -γ], with a
Gaussian PDF [2].
The general scaling law follows: MSD ~ MSDfreeμ, where MSDfree is the free particle MSD with the
particular basic dynamics.
(3) The file mean first passage time in the interval L, <FPT>, follows the scaling, <FPT> ~ <FPT>free f(L),
where f(L) upper bound is a linear function & lower bound, L1/2. We derive particular results [4].
(4) In the second talk, I will focus on files with anomalous basic dynamics, both renewal ones and
those that are not renewal. Results in these files follow:
In anomalous files that are renewal, namely, when all particles attempt a jump together, yet, with
jump times are taken from a distribution that decreases as a power law with an exponent, −1 − ε,
,the MSD scales like the MSD of the corresponding normal file, in the power of ε [5].
In anomalous files of independent particles, the MSD is very slow and scales like, MSD~log2(t).
Even more exciting, the particles form clusters in such files, defining a dynamical phase transition.
This depends on the anomaly power ε: the percentage of particles in clusters ξ follows, ξ=
[6]. Clustering is seen in files embedded in 2d, yet also.
I’ll yet also talk about applications of file dynamics in several areas in applied chemistry and
biophysics, including channels, membranes, etc.
References
[1] Flomenbom O. and Taloni A., On single-file and less dense processes, Europhys. Lett., 83
(2008) 20004.
http://www.flomenbom.net/EPL08.pdf
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[2] Flomenbom O., Dynamics of heterogeneous hard spheres in a file, Phys. Rev. E, 82 (2010)
031126.
http://www.flomenbom.net/NHFD_PRE_Journal.pdf
[3] Flomenbom, Ophir, Single File Dynamics Advances and a Focus on Biophysical Relevance,
Biophys. Rev. Lett., 2014, in press,
[4] Flomenbom Ophir, Mean First Passage Time in file dynamics, in preparation (2014).
[5] Flomenbom O., Renewal-anomalous-heterogeneous files, Phys. Lett. A, 374 (2010) 4331.
http://www.flomenbom.net/PLA_Journal_RHFD.pdf
[6] Flomenbom O., Clustering in anomalous files of independent particles, EPL 94, 58001 (2011).
http://www.flomenbom.net/epl13498-offprints.pdf
*2* Taloni Alessandro, Fabio Marchesoni
Interacting Single-file system: Fractional Langevin formulation and diffusion-noise approach
The latest advances in the analytical modelling of single file diffusion are discussed, starting from the
experimental evidence in real systems. A particular focus will be put on the derivation of the fractional
Langevin equation that describes the motion of a tagged file particle. Within this framework all the
statistical properties of any observable of interest can be calculated. In the last part, the connection
between the file density and the motion of the tagged particle will be discussed, and an alternative
derivation of the fractional Langevin equation starting from the diffusion-noise formalism will be
furnished.
*3* A.A.Vasylenko, V.R.Misko
The transport properties of electrons moving on superfluid 4He in narrow channels with
constrictions in quasi-one-dimensional and “quantum wire” regimes
The concept of single-file dynamics was first introduced in biophysics to account for the
transport of ions through molecular-sized channels in membranes [1]. This dynamical regime, which
refers to the motion of particles in a narrow quasi-one-dimensional channel where mutual passage is
forbidden, has been intensively studied in biology (e.g., ion-channel transport [2]) and physics.
Recently, the single-file dynamics regime was achieved in the system of electrons floating on the
surface of superfluid 4He in narrow channels with constrictions where the electrons form a one-
dimensional chain, or “quantum wire” [3, 4].
In order to achieve a better understanding of the phenomena observed in recent experiments
[3, 4], we employ molecular dynamics simulations to study the transport properties of electrons
driven by an external force on the surface of superfluid 4He in the “quantum wire” regime, when a
typical width of the channel is comparable to the inter-electron separation. We investigate the
dynamics of electrons in channels of different width such that they can accommodate from a few rows
of electrons to just one row, i.e., the crossover from quasi-1D to 1D regime. We consider channels
with various types of constrictions: single and multiple symmetric and asymmetric geometrical
Page | 14
constrictions with varying width and length, and saddle-point-type potentials with varying gate
voltage. We analyze the average particle velocity of the particles, vav, as a function of the driving force
or the gate voltage of the potential [5, 6]. We have revealed a significant difference in the dynamics of
electrons in long and short constrictions: the oscillations of the average velocity of the particles for the
systems with short constrictions exhibit a clear correlation with the transitions between the states
with different numbers of rows of particles; on the other hand, for the systems with longer
constrictions these oscillations are suppressed. These findings are in agreement with the experimental
observations by D.Rees et al. [4]. For a channel with asymmetric constrictions, we found a step-like
behavior of vav versus the constriction width [6]. On the other hand, we showed that a similar behavior
can be achieved when applying a transverse voltage to the channel. Thus our results contribute to the
understanding of the dynamics of electrons floating on the surface of superfluid 4He in channels with
constrictions and suggest a new effective tool for the control of the electron transport.
[1] A. L. Hodgkin and R. D. Keynes, The Potassium Permeability of a Giant Nerve Fibre. J. Physiol.
(London) 128, 61 (1955).
[2] D. A. Doyle, J. M. Cabral, R. A. Pfuetzner, A. Kuo, J. M. Gulbis, S. L. Cohen, B. T. Chait, and R.
MacKinnon, The Structure of the Potassium Channel: Molecular Basis of K+ Conduction and Selectivity.
Science 280(5360), 69 (1998).
[3] D. Rees and K. Kono, Transport of Electrons on Liquid Helium Across a Tunable Potential Barrier in
a Point Contact-like Geometry. J. Low Temp. Phys. 158, 301 (2010).
[4] D. G. Rees, H. Totsuji, and K. Kono, Commensurability-Dependent Transport of a Wigner Crystal in a
Nanoconstriction. Phys. Rev. Lett. 108, 176801 (2012).
[5] A.A. Vasylenko and V.R. Misko, Non-linear Transport of the Wigner Crystal on Superfluid 4He in a
Quasi-One-Dimensional Channel. Biophys. Rev. Lett. (2014), accepted.
[6] A.A. Vasylenko and V.R. Misko, Controlling the Transport of Electrons on Superfluid 4He in
Symmetric and Asymmetric FET-like Structures, arXiv:1401.8246v1, 31 Jan 2014.
*4* Tommy Dessup, Thibaud Maimbourg, Christophe Coste and Michel Saint Jean
Linear stability of a zigzag structure
The numerical and experimental realizations of systems of repealing particles, weakly confined in a 1D geometry, show a large diversity of equilibrium patterns. Experiments and simulations have been realized with ions confined in Paul's traps [1, 2, 3], paramagnetic colloidal particles and plasma dust optically confined [4, 5] and millimetric beads electrostatically interacting [6]. Among these observations, the homogeneous zigzag structures predicted by a simple by energetic analysis are indeed observed. Inhomogeneous patterns built of staggered row of few particles
surrounded by particles staying in a straight line, that we call "bubbles", are evidenced in many cases.
In order to understand the diversity of the observed patterns, we have studied the linear stability of
the homogenous zigzag structure, calculating the phonon spectrum. The apparition of unstable modes
in the zigzag structure can explain the observation of inhomogeneous patterns in the experiments. We
will present a lost of stability criterion allowing to map the expected patterns in function of the
physical properties of the system, such as the range of the inter-particle interactions.
Page | 15
Left : Stability diagram of a zigzag structure, in the plane φ (dimensionless wavenumber) and h (amplitude of the zigzag). Inset figures show the typical particle disposition in each domain. Right: Experimental observations of a linear configuration on top and of a bubble pattern at the bottom.
[1] J. P. Schiffer. Phase transitions in anisotropically confined ionic crystals. Phys. Rev. Lett., 70 :818, 1993. [2] G. De Chiara, A. del Campo, G. Morigi, M.B. Plenio, and A. Retzker. Spontaneous nucleation of structural defects in inhomogeneous ion chains. New Journal of Physics, 12 :115003, 2010. [3] M. Mielenz, J. Brox, S. Kahra, G. Leschhorn, M. Albert, and T. Schaetz. Trapping of topological- structural defects in coulomb crystals. Phys. Rev. Lett., 110 :133004, 2013. [4] A. Melzer. Zigzag transition of finite dust clusters. Phys. Rev. E, 73 :056404, 2006. [5] T. E. Sheridan and K. D. Wells. Dimensional phase transition in small yukawa clusters. Phys. Rev. E, 81 :016404, 2010. [6] C. Coste, J.-B. Delfau, C. Even, and M. Saint Jean. Single file diffusion of macroscopic charged particles. Phys. Rev. E, 81 :051201, 2010.
*5* Jörg Kärger Experimental Evidence of Single-File Constraints in Nanoporous Host-Guest Systems: Mysteries of Guest Diffusion in the Channel Network of Zeolites Owing to their crystallinity, zeolites with 1d-channel systems were recognized as attractive model systems for investigating mass transfer phenomena under single-file confinement. [1,2] As a consequence of the microscopic size of zeolite crystallites, the establishment of conditions for experimentally observing genuine single-file diffusion turns out to be quite a challenge. [3] This is, in particular, a consequence of the fact that the requirements for unbiased measurement of single-file diffusion are much more demanding [4] than for normal diffusion where it is sufficient to ensure that the crystal dimensions are large enough in comparison with the mean molecular displacements. It may be shown, however, that the more stringent requirement for recording molecular mean square
Page | 16
displacements following the time dependence of single-file diffusion may be abandoned with appropriately chosen boundary conditions [2]. The talk will introduce into the options provided by the techniques of microscopic diffusion measurement, notably by the pulsed field gradient technique of nuclear magnetic resonance (PFG NMR [2,5]) and by microimaging [6] via interference microscopy (IFM [7]) and IR microspectroscopy (IRM [8]). Diffusion measurements in zeolites prove to be a very sensitive tool for revealing deviations from the ideal text book structure which, in particular, are found to occur quite often with systems of supposed single-file structure [9]. Simultaneously with a continuous broadening of the spectrum of nanoporous host-guest systems of presumptive single-file structure, however, experimental evidence on the occurrence of genuine single-file diffusion is attained with increasing accuracy. [10] Hosting channel networks of quite different configuration, zeolites offer manifold options for investigating structure-mobility correlations in nanoporous host-guest systems. Examples include the inversion in the mean diffusion pathways by multi-component adsorption [6,11], observation of guest-induced framework transformations [6] and flux enhancement by counter-fluxes. [8] [1] J. Kärger, M. Petzold, H. Pfeifer, S. Ernst, J. Weitkamp, J. Catal. 1992, 136, 283–299. [2] J. Kärger, D. M. Ruthven, D. N. Theodorou, Diffusion in Nanoporous Materials, Wiley - VCH,
Weinheim, 2012. [3] a) V. Gupta, S. S. Nivarthi, A. V. McCormick, H. T. Davis, Chem. Phys. Lett. 1995, 247, 596–600; b)
K. Hahn, J. Kärger, V. Kukla, Phys. Rev. Lett. 1996, 76, 2762–2765; c) V. Kukla, J. Kornatowski, D. Demuth, I. Girnus, H. Pfeifer, L. V. C. Rees, S. Schunk, K. K. Unger, J. Kärger, Science. 1996, 272, 702–704;
[4] a) P. H. Nelson, S. M. Auerbach, Chem. Eng. J. 1999, 74, 43–56; b) C. Rödenbeck, J. Kärger, J. Chem. Phys. 1999, 110, 3970–3980;
[5] R. Kimmich, Principles of Soft-Matter Dynamics, Springer, London, 2012. [6] J. Kärger, T. Binder, C. Chmelik, F. Hibbe, H. Krautscheid, R. Krishna, J. Weitkamp, Nat Mater 2014,
13, 333–343. [7] L. Heinke, D. Tzoulaki, C. Chmelik, F. Hibbe, J. van Baten, H. Lim, J. Li, R. Krishna, J. Kärger, Phys.
Rev. Lett. 2009, 102, 65901. [8] C. Chmelik, H. Bux, J. Caro, L. Heinke, F. Hibbe, T. Titze, J. Kärger, Phys. Rev. Lett. 2010, 104,
85902. [9] a) E. Lehmann, S. Vasenkov, J. Kärger, G. Zadrozna, J. Kornatowski, Ö. Weiss, F. Schüth, J. Phys.
Chem. B 2003, 107, 4685–4687; b) E. Lehmann, S. Vasenkov, J. Kärger, G. Zadrozna, J. Kornatowski, J. Chem. Phys. 2003, 118, 6129–6132; c) F. Hibbe, C. Chmelik, L. Heinke, S. Pramanik, J. Li, D. M. Ruthven, D. Tzoulaki, J. Kärger, J. Am. Chem. Soc. 2011, 133, 2804–2807; d) L. Heinke, J. Kärger, Phys. Rev. Lett. 2011, 106, 74501;
[10] a) M. Dvoyashkin, A. Wang, S. Vasenkov, C. R. Bowers, J. Phys. Chem. Lett. 2013, 4, 3263–3267; b) M. Dvoyashkin, H. Bhase, N. Mirnazari, S. Vasenkov, C. R. Bowers, Anal. Chem. 2014, 86, 2200–2204;
[11] F. Hibbe, R. Marthala, C. Chmelik, J. Weitkamp, J. Kärger, J. Chem. Phys. 2011, 135, 184201-1-5.
*6* Henk van Beijeren
On the tight connection between collective and tagged particle motion in singe file dynamics
Single file dynamics is a generic term for the dynamics of one dimensional systems in which
neighboring particles cannot pass each other. A relation first proposed by Alexander and Pincus [1]
connects the mean square displacement of a tagged particle in such a system to the time evolution of
Page | 17
the collective density. In many cases this leads to a tagged particle mean square displacement
proportional to the square root of the MSD of collective excitations; e.g. in the case of regular
diffusion for the latter, the tagged particle MSD grows as t1/2 with time. But in cases where collective
excitations and tagged particle motion have different average drift velocities the tagged particle
always exhibits regular diffusion about its average drift.
For hamiltonian systems with short ranged interactions the tagged particle MSD is dominated by a
regular diffusion term proportional to t, due to sound mode contributions to the dynamics of the
collective density (in other words, the Brillouin peaks). In addition there is a contribution proportional
to t3/5, due to the heat mode contribution (the Rayleigh peak). Largely because of the one dimensional
structure, finite size effects are strong. Taking these into account one finds very good agreement
between theoretical predictions and computer simulations [2].
[1] S. Alexander and P. Pincus, Phys. Rev. B 18, 2011 (1978).
[2] H. Posch, private communications.
*7* A. Kr. Tripathi and Deepak Kumar
Correlations in Single File Diffusion: Open and Closed Systems We present a discussion of positional and velocity correlations of particles in single-file diffusion, based on some earlier work. We consider two physical situations: (a) An open system of N hard-core particles on an infinite line. (b) A large system with a fixed density of hard-core particles at an arbitrary temperature. In the first case (a), moments and correlations show unusual behavior. The average displacement of a particle is nonzero and grows as t1/2. Further it depends on the position of the particle. Particles on the right of center are pushed right and those on the left are pushed left. The mean-square displacement also depends on the position. The diffusion constant is small for particles around center but grows rapidly toward edges. Certain correlations in particle displacement grow with separation. For the second case (b) we give exact results for velocity-velocity auto-correlator of a tagged particle and establish that with time this correlator becomes negative and approaches zero as a power-law t-3/2 at long times. The mobility of the tagged particle is shown to decrease rapidly with density as has been observed in experiments.
*8* Ooshida, Takeshi, S. Goto, T. Matsumoto, A. Nakahara, & M. Otsuki
Collective motion in dense colloidal suspensions calculated with a two-dimensional version of the
Alexander-Pincus formula in a convected coordinate system
Diffusion in colloidal suspensions, modeled as two-dimensional or three-dimensional systems of
Brownian particles with some finite diameter, can become very slow when the density (the
volume fraction) is so large that every particle is confined in a "cage" that consists of its neighbors. An
analogous slowdown occurs also in one-dimensional setup (the single file diffusion), though it differs
in that the one-dimensional cage effect is present at any density. In both cases, as the cage effect
forbids free diffusion, the particles are compelled to remain motionless or move in some collective
Page | 18
manner.
As an indicator of such collective motion, here we calculate the two-particle displacement
correlation. The calculation relies on adoption of the convected coordinate system (also known by the
name of the label variable or the Lagrangian description), which is a curvilinear coordinate system that
moves together with the material and plays the role of an infinite number of tags. Utilizing this
convected coordinate system, we can relate the displacement correlation to the temporal correlations
of the hydrodynamic quantities such as the density or the velocity.
In the one-dimensional case [1,2], the convected coordinate system is simply a continuum analog of
the particle numbering. The relation between the displacement correlation and the one-dimensional
density field turns out to be essentially the same as the formula by Alexander and Pincus [3], except
for delicate improvement that makes the formula asymptotically exact for large systems: instead of
the Eulerian correlation of the density, our version of the formula uses the Lagrangian correlation of
the vacancy. Subsequently, we develop a two-dimensional version of the Alexander-Pincus formula,
relating the displacement correlation to the temporal correlation of the deformation gradient tensor
[2,4]. As a result, we obtain a flow pattern with a pair of swirls, similar to the one obtained from
particle-based numerical simulations [4,5]. The theoretical calculation also suggests that the mean-
square displacement is a sum of a linear term (normal diffusion) and a logarithmic correction, being
qualitatively consistent with a precedent result in two-dimensional lattice systems [6].
[1] Ooshida et al.: J. Phys. Soc. Jpn. 80, 074007 (2011)
[2] Ooshida et al.: Phys. Rev. E 88, 062108 (2013); arXiv:1212.6947
[3] Alexander & Pincus: Phys. Rev. B 18, 2011 (1978)
[4] Ooshida et al.: (in preparation)
[5] Doliwa & Heuer: Phys. Rev. E 61, 6898 (2000)
[6] van Beijeren & Kutner: Phys. Rev. Lett. 55, 238 (1985)
*9* C Kreuter1, F Shaban1, M Ashari1, T Lorenz1, D G Rees2, K Kono3, E Scheer1, A Erbe4, P Leiderer1 1 University of Konstanz, Germany, 2 NCTU, Taiwan, 3 RIKEN, Japan, 4 Helmholtz-Center Dresden-Rossendorf, Germany
Transport of Surface State Electrons on liquid helium through narrow channels
We have used a Source-Gate-Drain configuration with electrons on liquid helium (the “Helium FET” [1,2]) to study the transport of “classical” electrons through narrow channels. The channels, formed by the split gate of the device, were between ten and a few hundred µm long and several µm wide, and could be blocked completely by a negative bias voltage applied to the gate. In contrast to previous experiments, where the electron densities in Source and Drain were nearly the same and the system therefore was close to equilibrium, in the present measurement the Drain was empty. The transport of the electrons through the channel was initiated by opening the gate with a short positive pulse with a duration down to nanoseconds, and the amount of electrons which passed during this time was registered. In this way, we could determine for the first time the transport properties of such a system on a nanosecond time scale and far off equilibrium. The data show that in addition to the externally applied electric driving field also the mutual Coulomb repulsion between the electrons influences the transport. Moreover, clear indications for the formation of lanes of electrons in the channels are observed. In addition to these measurements at low temperature we have carried out complementary experiments at ambient conditions with a model system consisting of colloidal particles with well-
Page | 19
defined size, suspended in water and moving in lithographically prepared channels. The particles had a diameter of some 5µm and were superparamagnetic, such that their magnetic dipole interaction could be tuned by the application of an external magnetic field. The motion of these particles in channels with a width of several ten µm was registered by video microscopy. Transport studies of these systems also showed clear examples of lane formation [3], furthermore oscillating behavior between quasi-single file diffusion and normal diffusion [4], and in the case of channels with one or two obstacles the thermally activated transport over barriers and through islands [5]. References: [1] J. Klier, I. Doicescu, and P. Leiderer: "First dc measurements of electrons on liquid He: the helium-FET", J. Low Temp. Phys. 121, 603 (2000) [2] M. Ashari, D.G. Rees, K. Kono, E. Scheer, P. Leiderer: The Helium Field Effect Transistor (I): Storing Surface State Electrons on Helium Films, J. Low Temp. Phys. 167, 15 (2012) [3] M. Köppl, P. Henseler, A. Erbe, P. Nielaba, and P. Leiderer: Layer Reduction in Driven 2D-Colloidal Systems through Microchannels, Phys. Rev. Lett. 97, 208302 (2006) [4] U. Siems, C. Kreuter, A. Erbe, N. Schwierz, S. Sengupta, P. Leiderer, P. Nielaba: Non-monotonic crossover from single-file to regular diffusion in micro-channels, Scientific Reports 2, 1015 (2012) [5] C. Kreuter, U. Siems, P. Nielaba, P. Leiderer, and A. Erbe: Transport phenomena and dynamics of externally and self-propelled colloids in confined geometry, Eur. Phys. J. Special Topics 222, 2923 (2013)
*10* David G. Rees1, 2 and Kimitoshi Kono2 NCTU-RIKEN Joint Research Laboratory, Institute of Physics, National Chiao Tung University, Hsinchu, Taiwan
1, Low
Temperature Physics Laboratory, RIKEN, Wako-shi, Japan2
Single-File Transport of Classical Electrons on the Surface of Liquid Helium
Electrons trapped on the surface of liquid helium form a model two-dimensional electron system [1].
Because the electron density is low (~109 cm-2 interaction between the electrons is essentially
unscreened, the system can be regarded as a strongly correlated classical analogue of the degenerate
Fermi gas. Electrons on helium have therefore long been used to study many-body phenomena in two
dimensions, perhaps most notably the formation of the classical Wigner crystal at low temperatures
[2].
Here we review recent experiments investigating the transport of electrons on helium through
microscopic constrictions [3]. The constrictions are formed in microchannels filled with liquid helium
and are controlled electrostatically using gate electrodes. Two constriction geometries are studied;
short saddle-point constrictions in which the width is comparable to the length, and long constrictions
in which the length greatly exceeds the width. In both cases, the constriction width can be tuned so
that the electrons move through the constriction in single file; in the long channel, we are able to
isolate several hundred particles in a single chain.
As the width of the short constriction is increased, a periodic suppression of the electron current is
observed due to pinning for commensurate states of the electron lattice [4]. A related phenomenon is
observed for the long constriction whereby the quasi-one-dimensional Wigner lattice exhibits
reentrant melting as the number of electron chains increases [5]. Our results demonstrate that
electrons on helium are an ideal system in which to study classical phase transitions and many-body
transport phenomena in confined geometries.
Page | 20
[1] E. Andrei, Ed., “Two-Dimensional Electron Systems on Helium and Other Cryogenic Substrates”,
Kluwer Academic, Dordrecht, 1997.
[2] C. C. Grimes and G. Adams, “Evidence for a Liquid-to-Crystal Phase Transition in a Classical, Two-
Dimensional Sheet of Electrons”, Physical Review Letters, Vol. 42, No. 12, 1979, pp. 795-798.
[3] D. G. Rees et al., “Point-Contact Transport Properties of Strongly Correlated Electrons on Liquid
Helium”, Physical Review Letters, Vol. 106, No. 2, 2011, pp. 026803-1-4.
[4] D. G. Rees, H. Totsuji and K. Kono, “Commensurability-Dependent Transport of a Wigner Crystal in
a Nanoconstriction”, Physical Review Letters, Vol. 108, No. 17, 2012, pp. 176801-1-4.
[5] H. Ikegami, H. Akimoto, D. G. Rees and K. Kono, “Evidence for Reentrant Melting in a Quasi-One-
Dimensional Wigner Crystal”, Physical Review Letters, Vol. 109, No. 23, 2012, pp. 236802-1-5.
*11* C. Coste, J.-B. Delfau, M. S. Jean
Longitudinal and Transverse Single File Diffusion in Quasi-1D Systems We review our recent results on Single File Diffusion (SFD) of a chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We exhibit new behaviors specifically associated to small systems and to small damping. The fluctuations dynamics is explained by the decomposition of the particles motion in the normal modes of the chain. For longitudinal fluctuations, we emphasize the relevance of the soft mode linked to the translational invariance of the system to the long time SFD behavior. We show that close to the zigzag thresh-old, the transverse fluctuations also exhibit the SFD behavior, characterized by a mean square displacement that in-creases as the square root of time. This cannot be explained by the single file ordering, and the SFD behavior results from the strong correlation of the transverse displacements of neighboring particles near the bifurcation. Extending our analytical modeling, we demonstrate the existence of this subdiffusive regime near the zigzag transition, in the thermodynamic limit. The zigzag transition is a supercritical pitchfork bifurcation, and we show that the transverse SFD behavior is closely linked to the vanishing of the frequency of the zigzag transverse mode at the bifurcation threshold.
*12* M.A. Lomholt
Universality and non-universality of mobility in heterogeneous single-file systems
In this talk I will discuss tracer particle mobility in single-file systems with random friction constants. It
will be found that for distributions of frictions which possess a finite average the tracer particle will
behave universally for long times in the same way as the case of a single-file with identical particles.
For heavy tailed power-law distributions of frictions it is found that no self-averaging occurs even at
long times and the behavior thus becomes non-universal [1].
[1] M.A. Lomholt, and T. Ambjornsson, Universality and nonuniversality of mobility in heterogeneous
single-file systems and Rouse chains, Phys. Rev. E 89, 032101 (2014).
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*13* Artem Ryabov
Single-file system with absorbing boundary: Tracer dynamics and first-passage properties.
We address the single-file diffusion in the presence of an absorbing boundary. The emphasis is on an
interplay between the hard-core interparticle interaction and the absorption process. The exact
probability density function for the position of a tagged particle is derived by means of probabilistic
arguments. First, starting from this exact probability density, the long-time asymptotic dynamics is
studied. The mean position, the mean squared displacement and the decay of the survival probability
are controlled by dynamical exponents which depend on the initial order of the tagged particle in the
file. Second, conditioning on nonabsorption, we investigate the distribution of long-lived particles. In
this conditional framework, the dynamical exponents are the same for all particles, however, a given
tagged particle possesses an effective diffusion coefficient which depends on its initial order. Third,
after performing the thermodynamic limit, the conditional dynamics of the tracer becomes
subdiffusive, the generalized diffusion coefficient $D_{1/2}$ being different from that reported for the
system without absorbing boundary.
ACKNOWLEDGMENTS: AR acknowledges a financial support by the grant SVV-2014-260093.
REFERENCES:
[1] A. Ryabov and P. Chvosta, Tracer dynamics in a single-file system with absorbing boundary, Phys.
Rev. E 89, 022132 (2014)
[2] A. Ryabov, Single-file diffusion in an interval: first-passage properties, J. Chem. Phys. 138, 154104
(2013)
[3] A. Ryabov and P. Chvosta, Survival of interacting Brownian particles in crowded one-dimensional
environment, J. Chem. Phys. 136, 064114 (2012)
*14* Luciano Moffatt & Jerónimo Auzmendi
Kinetic Information out of macroscopic fluctuations Ligand gated channels couple neurotransmitter binding to the opening of the pore. In this talk, three aspects related to obtaining kinetic information out of macroscopic fluctuations will be presented. 1) the activation mechanism of purinergic receptors will be studied by applying the molecular agonist in very short pulses1. In this way, the binding of the agonist finished before all the channels open. From those experiments a short lived intermediate state between closed and open lasting 100 microseconds was detected. Three alternative kinetic schemes accurately describe the results, two of them explain the cooperative nature of the lingand binding and suggest plausible activation mechanisms. 2) The inverse problem: given a series of experimental results and given a tentative kinetic scheme, how can I find the combination of kinetic rates, channel conductance and number of channels that better describe them. The solution of this problem involves applying Bayesian statistics to the analysis of Hidden Markovian Chains2. In this way the likelihood function of the kinetic parameters can be determined for macroscopic currents. 3) Recent advances in the generation of even shorter pulses will be communicated. Using a faster piezo device, a custom build power source (100V, 10A ,50KHz) we generated very fast movements of the interface between control and experimental solutions. Pulsed stimulation of the piezo resulted in a complex movement of the interfase. After measuring the transfer function of the whole system, the command voltage applied to
Page | 22
the piezo could be optimized and pulses that lasted only 30 microseconds were generated3. In this way we are closer to experimentally study the activation of the fastest ion channels 1. Journal of General Physiology vol. 130, No. 2, 183-201 2. Biophysical Journal 93 (1) 74-91. 3. PLoS One. 2012;7(8):e42275. *15* Bert de Groot The molecular dynamics of single file ion and water permeation.
What is the mechanism of single-file water permeation through specialized channels? What are the
molecular determinants of channel permeation and gating? How do ions permeate selective ion
channels? Can we design specific membrane channel inhibitors? What is the antimicrobial mechanism
of the human antibiotic dermcidin? These are some of the questions that are addressed at the atomic
level by molecular dynamics simulations.
[1] Sören J. Wacker, Camilo Aponte-Santamaria, Per Kjellbom, Soren Nielsen, Bert L. de Groot, Michael
Rützler. The identification of novel, high affinity AQP9 inhibitors in an intracellular binding site.
Molecular Membrane Biology 30:246-260 (2013).
[2] Ulrich Zachariae, Robert Schneider, Rodolfo Briones, Zrinka Gattin, Jean-Philippe Demers, Karin
Giller, Elke Maier, Markus Zweckstetter, Christian Griesinger, Stefan Becker, Roland Benz, Bert L. de
Groot, and Adam Lange. Beta-barrel mobility underlies closure of the voltage-dependent anion
channel. Structure. 20:1540-1549 (2012).
[3] Chen Song, Conrad Weichbrodt, Evgeniy S. Salnikov, Marek Dynowski, Björn O. Forsberg, Burkhard
Bechinger, Claudia Steinem, Bert L. de Groot, Ulrich Zachariae, and Kornelius Zeth.Crystal structure
and functional mechanism of a human antimicrobial membrane channel. Proc. Nat. Acad. Sci. 110:
4586-4591 (2013).
[4] Carsten Kutzner, Helmut Grubmüller, Bert L. de Groot, Ulrich Zachariae. Computational
Electrophysiology: The Molecular Dynamics of Ion Channel Permeation and Selectivity in Atomistic
Detail. Biophys. J. 101: 809-817 (2011).
[5] Jochen S. Hub and Bert L. de Groot. Mechanism of selectivity in aquaporins and aquaglyceroporins.
Proc. Nat. Acad. Sci. 105:1198-1203 (2008).
Page | 23
*16* Simon K. Schnyder, Markus Spanner, Felix Höfling, Thomas Franosch*, Jürgen Horbach
*email: [email protected]
Rounding of the localization transition in model crowded media
Transport in dense environment can be significantly suppressed and even become anomalous. Here
we investigate obstructed transport in two dimensions by computer simulation for increasingly
complex frozen host structures to test if the predictions of the localization transition in the Lorentz
model apply.
We introduce hard-core correlations in the cherry-pit model, and employ a soft potential model for
realistic interactions of a frozen liquid. We observe anomalous transport of an ideal gas of tracer
particles in these structures up to several decades in time. This and the suppression of diffusion is
attributed to an underlying percolation transition. The rounding of the transition observed in the soft
potential model can be understood as an average over the tracers -- each with its own critical density.
*17* Giuseppe B. Suffritti,
“Problems in modelling single-file diffusion of water adsorbed in zeolites: computer simulations and
comparison with recent theory”
When simulating the behaviour of water in the straight nano-channels of two zeolites (nanoporous
aluminosilicates), where the water molecules are subject to a sinudoisal potential, we found that, the
diffusive process was of single-file type, and that the propagator at high concentration is
approximately Gaussian but is multimodal at higher concentration. The former situation can be
interpreted by current single-file diffusion theories, but the latter is still waiting for a complete
theoretical treatment. In particular, a detailed comparison between simulation results and theoretical
formulations is shown for the approximate treatment by Taloni and Lomholt [1] based on a fractional
Langevin equation with a special noise mimicking the single-file motion constraint, as well as by Lizana
and Ambjörnsson [2], who published an exact solution of the single-file diffusion problem for a finite
system of hard-core interacting particles with reflecting boundaries, stemming from the Bethe ansatz.
Problems and suggestions for the complete solution of the single-file problem for particles subject to a
periodic potential are finally proposed.
[1] A. Taloni and M. A. Phys. Rev. E 78 ,051116 (2008)
[2] L. Lizana and T. Ambjörnsson, Phys .Rev. Lett. 100 ,200601 (2008)
*18* Karolis Misiunas
Anisotropic diffusion of spherical particles in closely confining microchannels
We present here the measurement of the diffusivity of spherical particles closely confined by narrow
microchannels [1]. Our experiments yield a two-dimensional map of the position-dependent diffusion
Page | 24
coefficients parallel and perpendicular to the channel axis with a resolution down to 129 nm. The
diffusivity was measured simultaneously in the channel interior, the bulk reservoirs, as well as the
channel entrance region. In the channel interior we found strongly anisotropic diffusion [2]. While the
perpendicular diffusion coefficient close to the confining walls decreased down to approximately 25%
of the value on the channel axis, the parallel diffusion coefficient remained constant throughout the
entire channel width. In addition to the experiment, we performed finite element simulations for the
diffusivity in the channel interior and found good agreement with the measurements. Our results
reveal the distinctive influence of strong confinement on Brownian motion, which is of significance to
microfluidics as well as quantitative models of facilitated membrane transport. We further extend our
study by considering diffusion of multiple particles inside a microfluidic channels.
[1] S. Pagliara, C. Schwall, and U. F. Keyser, "Optimizing Diffusive Transport Through a Synthetic
Membrane Channel", Advanced Materials, 25, 844-849 (2013).
[2] S. L. Dettmer, K. Misiunas, S. Pagliara, and U. F. Keyser, "Anisotropic diffusion of spherical particles
in closely confining microchannels", Phys. Rev. E, accepted (2014).
*19* Elchin Huseynov, Adil Garibov, Ravan Mehdiyeva
Instiute of Radiation Problems of Azerbaijan National Academy of Sciences, AZ 1143, B.Vahabzadeh 9,
Baku, Azerbaijan, [email protected], [email protected]
About nano silica impedance: Effect of neutron flux on the real and imaginary parts of impedance of nano-grained silica.
Silica has wide application branches for different purposes. Silicon oxide compounds are of
great significance in cosmic and nuclear technology. In recent years, many properties were discovered,
e.g.: the properties that affect the particles’ sizes. Therefore, nano-sized samples of SiO2 classic oxide
dielectric are again in the spotlight of researchers. Studies check the influence of ionizing rays on
physical and surface physical-chemical properties of nano SiO2 and proposals are being elaborated on
application of these sized samples in different fields.
Impedance of nano silica at different temperatures has been studied in the work, Refs. [1-
12]. It has been revealed from the analysis of the experimental results that though the dependence of
impedance on irradiation period is not obviously observed at low temperatures (100K and 200K), at
high temperatures it is clealry seen. According to Cole-Cole diagram, it has been calculated relaxation
periods in the samples. In the figure, we show the complex impedance plots of nano silica at 400K
value of temperature, within the initial state and various neutron flux periods (Fig.1). It has been
determined that with the increase of the irradiation period, the polarization and relaxation period
decreases. The clusters appearing in the sample under neutron flux influence cause polarization to be
chaotic at low temperatures (~100K) in surface charges in the system. Yet at high temperatures (300-
400K), these clusters disappear.
Page | 25
[1] E.M.Huseynov, A.A.Garibov, R.N.Mehdiyeva “Calculation of the specific surface area of SiO2
nanopowder and getting nano-SiO2-H2O systems” Azerbaijan Journal of Physics ISSN 1028-8546,
Volume XIX, Number 1, p. 10-14, Azerbaijan 2013
[2] E.M. Huseynov, A.A.Garibov, R.N.Mehdiyeva, “Synthesis methods of nano SiO2 powder”
Transactions of National Academy of Sciences of Azerbaijan, Series of Physics – Mathematical and
Technical Sciences, Physics and Astronomy, ISSN 0002-3108 Vol. XXXII N5, p 83-88/152, Azerbaijan
2012
[3] E.M.Huseynov, N.A.Novruzov “DTA and TG analysis of nano SiO2 - H2O systems” New Challenges in
the European Area: Young Scientist’s 1st International Baku Forum p. 150-151, Azerbaijan 2013
[4] Luka Snoj, Gasper Zerovnik, Andrej Trkov, Applied Radiation and Isotopes 70, 483–488 (2012)
[5] L. Snoj, A. Trkov, R. Jačimović, P. Rogan, G. Žerovnik, M. Ravnik, Appl. Radiat. Isotopes, Vol. 69, 136-
141 (2011)
[6] Luka Snoj, Andrej Kavcic, Gasper Zerovnik, Matjaz Ravnik, Ann. Nucl. Energy, 37 (2), 223–229
(2010)
[7] Luka Snoj, Andrej Trkov, Matjaz Ravnik, Gasper Zerovnik, Ann. Nucl. Energy 42, 71–79 (2012)
[8] Luka Snoj, Matjaž Ravnik, Nuclear Engineering and Design, Volume 238, Issue 9, 2473-2479 (2008)
[9] Jazbec Anze, Zerovnik Gasper, Snoj Luka, Trkov Andrej, Atw. Internationale Zeitschrift für
Kernenergie, iss. 12, vol. 58, 701-705 (2013)
[10] Vladimir Radulović, Žiga Štancar, Luka Snoj, Andrej Trkov, Applied Radiation and Isotopes, Volume
84, 57-65 (2014)
[11] Gasper Zerovnik, Manca Podvratnik, Luka Snoj, Ann. Nucl. Energy 63, 126–128 (2014)
[12] V.Bobnar, A.Erste, X.Z.Chen, C.L.Jia and Q.D.Shen, Phys. Rev. B 83, 132105 (2011)
*20* Paul Higgs
Linking Ribosome Dynamics to Molecular Evolution
In many bacterial genomes there is preferential use of codons that are more rapidly translated. Codon usage evolves alongside other adaptations for fast and efficient protein synthesis, such as duplication of genes for ribosomal RNA and transfer RNA. Which codons are preferred in an organism depends on the nature of the codon-anticodon interaction and the frequency of the corresponding tRNAs. The position of slow codons in a gene can affect the speed of translation, in some cases causing queuing of ribosomes. We will present a theory to predict the rate of translation of a given gene sequence as a
Figure1. Figure1. Complex impedance plots
of nano silica at 400K value of temperature,
within initial state (c.s.) and various neutron
flux (5h, 10h, 15h and 20h) periods. (Real (Re
Z') and Imaginary (Im Z'') part of impedance).
Axes in units of resistance 10^7 ohm.
Page | 26
function of the speeds of translation of the individual codons and the density of ribosomes bound to the mRNA. The secondary structure in mRNAs also influences ribosome dynamics. We will discuss the way that selection in favour of either weaker or stronger secondary structure influences the frequencies of codons in different parts of a gene sequence. It appears that avoidance of strong secondary structure close to the beginning of a gene is important to allow ribosomes to initiate translation and this seems to act against the selection for fast codons that operates in the rest of the gene sequence.
*21* Kwinten Nelissen1 , T. Becker2 , Bart Cleuren2 , B. Partoens1 , C. Van den Broeck2 1Universiteit Antwerpen, 2020 Antwerp, Belgium,
2 Hasselt University, 3590 Diepenbeek, Belgium
Diffusion of interacting particles in discrete Geometries
We evaluate the self-diffusion and transport diffusion of interacting particles in a discrete geometry
consisting of a linear chain of cavities, with interactions within a cavity.Confinement is introduced by
limiting the number of particles on a lattice site. The effect of correlations is elucidated by comparison
with numerical results. Quantitative agreement is obtained with recent experimental data for
diffusion in a nanoporous zeolitic imidazolate framework material, ZIF-8. Further the adsorption and
desorption kinetics is presented.Adsorption and desorption are found to proceed at different rates,
and are strongly influenced by the concentration dependent transport diffusion. At last the role of
current fluctuations are presented.
*22* Janusz Gajda
Applications of tempered α-stable processes in physics
In many physical systems we observe a transition from the initial subdiffusive character of motion (α <
1) to the standard linear in time mean-squared displacement (MSD) for long times (α = 1). The
coexistence of subdiffusion and normal diffusion was empirically confirmed in a number of systems,
i.e. in a random motion of bright points associated with magnetic fields at the solar photosphere [1].
The transition from anomalous to normal diffusion was also observed in the motion of molecules
diffusing in living cells [2, 3].
In order to capture such behavior, we use tempered α-stable distributions to model processes
exhibiting transition from anomalous to normal motion under influence of external space-dependent
force fields. We present generalized versions of Fractional Fokker-Planck equation (FFPE) and
Fractional Klein-Kramers equation (FKKE) where the generalization consist in the appropriate
truncation of the heavy-tailed α-stable waiting times in the underlying continuous-time random walk
(CTRW) scenario. More generally we consider also the case of transient subdiffusion.
The work is based on the series of papers [4, 5, 6].
[1] A.C. Cadavid, J.K. Lawrence, and A.A. Ruzmaikin, Astrophys. J. 521, 844 (1999).
[2] M. Platani, I. Goldberg, A.I. Lamond, and J.R. Swedlow, Nat. Cell Biol. 4, 502 (2002).
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[3] K. Murase, T. Fujiwara, Y. Umemura, K. Suzuki, R. Iino, H. Yamashita, M. Saito, H. Murakoshi, K.
Ritchie, and A. Kusumi, Biophys. J. 86, 4075 (2004)
[4] J. Gajda, M. Magdziarz, Phys. Rev. E 82, 011117 (2010).
[5] J. Gajda, M. Magdziarz,Phys. Rev. E 84, 021137 (2011).
[6] J.Gajda, A.Wy loma nska, Physica A 405, 104 (2014).
*23* Lorin Milescu
From single molecules to cells: testing ion channel models in live neurons.
Brain function depends on intrinsic neuronal excitability, which in turn is a function of ion channel activity in the membrane. A powerful paradigm for studying the relationship between neuronal firing patterns and membrane currents in individual neurons is to combine the patch clamp recording technique with real-time computation. The principle is to pharmacologically block the current of interest, and then functionally replace it with an injected current, dynamically calculated on the basis of an ion channel kinetic model. The neuron makes no distinction between the native current and the model-based current. Thus, the sensitivity of the firing pattern to the dynamic properties of the current can be studied by varying the properties of the model and manipulating the model-based current in real-time. A hybrid construct can be created with the dynamic clamp technique, where a biological component of a real neuron has been functionally replaced or modified by a computational model. Modeling a single current against a background of uncharacterized ionic conductances is potentially more accurate than mathematical simulations, where in principle every current must be well characterized, and more versatile than pharmacological approaches, limited by the available drugs. Of particular interest to our laboratory is the contribution of voltage-gated Na+ channels to the spiking activity of pacemaker mammalian central neurons. We developed real-time computational algorithms and software that allow us to model the complex gating properties of Na+ channels, and to study the role played by the Na+ current during the spiking cycle.
*24* Remigijus Lape
On the activation mechanism of pentameric ligand-gated ion channels
Pentameric ligand-gated channels are members of a big nicotinic receptor family. They are activated upon binding of neurotransmitters such as acetylcholine, glycine or GABA and mediate most of the fast synaptic transmission in the central and peripheral nervous system. These ion channels are formed of a variety of subunits, which give rise to a distinct pharmacological and physiological profile of each receptor. How exactly the signal is transmitted from the ligand binding site to the gate of the pore is under intense study; however, a coherent view of how gating occurs still remains elusive. Each of these multimeric ion channels are composed of a couple of thousand amino acids. Protein molecules are in continuous structural fluctuation, covering timescales that range from picoseconds to milliseconds. The timescale depends on the size of the structural elements involved in the motion. This ranges from single atoms, to the side chains of single amino acids, to several amino acids moving in a coordinated pattern. Larger scale conformational changes overcome higher energy barriers and give rise to a few stable conformational states.
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Advances in high resolution recording of single channel activity allow us routinely to collect
observations that contain a wealth of information about conformational states with lifetimes as short
as a few microseconds. This led us to explore more and more detailed activation mechanisms of
ligand gated receptors. These detailed mechanisms are likely to be a more realistic description of the
energy landscape of channel proteins than any previously available for these or other proteins. On the
other hand, the complexity of these mechanisms challenges our mathematical and computational
techniques. In this talk I will overview current ideas about activation mechanisms in the nicotinic
receptor family.
*25* Eli Barkai
Single file diffusion: the role of initial conditions and external forces. We discuss a general formula relating between the mean squared displacement of a tagged particle in single file diffusion, and the single (non-interacting) reflection probability R [1]. This formula relates the non-interacting Green function, in the presence of external forces acting on all the particles and the initial conditions with the tagged particle fluctuations. Rich physical behaviors emerge which depend on the time scale, the underlying free dynamics, and the force field [2]. In an open system and in the absence of forces we discuss the ever-lasting influence of initial conditions on the transport coefficients of single file diffusion [3]. This leads to violation of Einstein relations and subtle difference between time and ensemble averages, i.e. the ergodic properties of single file diffusion are not trivial due to everlasting memory of the initial state of the system [3]. [1] E. Barkai, R. Silbey, Theory of Single File Diffusion in a Force Field, Phys. Rev. Lett. 102 050602 (2009). [2] E. Barkai, R. Silbey Diffusion of Tagged Particle in an Exclusion Process, Physical Review E 81, 041129 (2010). [3] N. Leibovich, E. Barkai Everlasting effect of initial conditions on single file diffusion Phys. Rev. E, 88, 032107 (2013)
*26* John E Pearson
A Data-Driven Approach to Constructing a Kinetics Model of the IP3 Receptor/Ca2+ Channel in SF9 Cells The IP3 Recptor/Ca2+ channel (IP3R) is a calcium ion channel. I will describe our efforts at obtaining a kinetic model for this complex p(1.2M Dalton) protein from patch clamp data. The kinetics of the IP3R depend on two ligands; inositol trisphoshate (IP3) and calcium. The goal was to try to extract a discrete state Markov chain for the kinetics of opening and closing that incorporated both equilibrium and non-equilibrium data and that captured the modal gating. We imposed very few structurally based constraints as we felt such constraints, although widely employed in the field, do not have a solid physical basis. (Frauenfelder et al noted that: “the protein is not a rigid system in which a ligand
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moves in a fixed potential. Rather there is a strong mutual interaction between ligand and protein... A protein is not like a solid house into which the visitor (the ligand) enters by opening doors without changing the structure. Rather it is like a tent into which a cow strays.”) Thus the binding of ligands can dramatically alter the structure of a protein. The plan was to assume the validity of mass action kinetics for the binding/unbinding of the two ligands and of detailed balance and then to obtain a reasonably predictive model of the kinetics via unsupervised machine learning. We did not succeed in the unsupervised aspect although we did in fact obtain a kinetic scheme that seemed in reasonable accord with both the data that we used to learn the model as well as with out of sample data. We compare the statistical fit of our model to data to the de Young Keizer model which is widely used in the literature.
*26C* John E Pearson
Messages Do Diffuse Faster than Messengers: Reconciling Disparate Estimates of the Morphogen
Bicoid Diffusion Coefficient
The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila
embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at
the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within
this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This
coefficient has been measured utilizing two optical techniques, Fluorescence Recovery After
Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which
the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following
questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model
explain Bcd gradient formation within the experimentally observed times? In the work, we present a
simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the
FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient
formation. The discrepancy arises from the fact that FCS and FRAP report on
different effective (concentration dependent) diffusion coefficients, one of which describes the
spreading rate of the individual Bcd molecules (the messengers) and the other one that of their
concentration (the message). The latter is the one that is more relevant for the gradient establishment
and is compatible with its formation within the experimentally observed times.
*27* Cécile Fradin, Daniel Banks, Charmaine Tressler, Robert Peters
Setting apart anomalous from simple diffusion - and everything in between – utilizing variable
length-scale measurements
Macromolecular diffusion in cells and complex fluids is often found to deviate from simple Brownian
diffusion. One possible explanation for this behavior is that molecular crowding or molecular
interactions renders the diffusion anomalous, where the mean-squared displacement of the particles,
instead of being proportional to time, scales as a slower power law in time. Unfortunately, methods
commonly used to study cellular dynamics, such as fluorescence correlation spectroscopy (FCS) or
fluorescence recovery after photobleaching (FRAP), probe diffusion only over a very narrow range of
length-scales. Thus they cannot directly test the dependence of the mean-squared displacement on
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time. Here we discuss experimental results obtained with a newly introduced variant of FCS, variable
length-scale FCS (VLS-FCS), where the volume of observation is varied over several orders of
magnitudes, and show that it can provide a strong test for theories of anomalous diffusion. In the case
of dense agarose gels, our results are consistent with anomalous diffusion.Yet, for sparse agarose gels
and for crowded dextran solutions, we observed a discrepancy between single-scale FCS
measurements, which clearly show a deviation from simple diffusion, and VLS-FCS experiments, which
showed the mean-squared displacement is proportional to time. This calls to mind the "anomalous yet
Brownian" diffusion recently reported in other systems.
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POSTERS
*1* Anna Vasylenko, The transport properties of electrons moving on superfluid 4He in narrow channels with constrictions in quasi-one-dimensional and “quantum wire” regimes *2* Tommy Dessup, Linear stability of a zig-zig structure
*3* Lucena Diego, Single-file and normal diffusion of magnetic colloids in modulated channels
*4* Kwinten Nelissen, Diffusion of Interacting Particles in Discrete Geometries
*5* Gajda Janusz, Applications of tempered α-stable processes in physics
*6* Karolis Misiunas, Anisotropic diffusion of spherical particles in closely confining microchannels
Short lecture presenters:
*** #5 from the poster presenters list is confirmed at printing, (perhaps will present others from: 1,
3, 5).
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ETTORE MAJORANA FOUNDATION AND CENTRE FOR SCIENTIFIC CULTURE
INTERNATIONAL SCHOOL ON STATISTICAL PHYSICS
GENERAL INFORMATION
How to reach Erice. A limousine or a bus of the Ettore Majorana Centre (EMCSC) will
be available provided you have properly filled and returned the Travel Form by the date
announced on the Course website). On your arrival at the airport or railway station look for
the driver of the EMCSC who is waiting for you and will drive you to Erice. He will be there
holding the poster of the International School of Statistical Physics.
Missing driver. In case the driver is not there within half an hour after my arrival, you
can call the Secretariat of the EMCSC (phone no.: 0923 869133) for instructions. Phone cards
may be purchased at the news-stand. NB: the cost of a trip to Erice by taxi may not be
reimbursed unless the trip has been authorized by the EMCSC. In the case of an emergency
you can call one of the Directors (phone no: +39 320 7985898)
Check-in. On your arrival at the reception desk please fill the registration form; you
will be escorted to your accommodation. You also will be given a conference package and an
EMCSC badge. The reception desk is located at the EMCSC main building (San Rocco).
Badge. Please carry you badge at all tims, inside the EMCSC as well as outside,
especially at restaurants, during excursions, social events and shopping.
Restaurants At the restaurants associated with EMSCS meals are free – you just have
to show your badge and sign a list provided by the restaurant. Beverages and meals not
included in the EMCSC menu are extras and should be paid for. The choice among the
associated restaurants is absolutely free. Thus, if you need a special food (vegetarian, kosher,
etc.), you can negotiate it directly with the restaurant (the EMSCS staff will be glad to offer
their assistance).
Fee Unless you have been awarded a full grant or your Institution has already paid
your fee by a money order to EMCSC, you re requested to pay your fee after registration
directly at the Course Secretariat (and not at the reception desk). Payments should be either
cash or by traveler cheques, in Euros (US dollars, UK pounds or Swiss francs are all right).
Credit cards and personal cheques are not accepted. Accepted applicants are supposed to
stay the whole period of the course.
Accompanying persons Rooms in Erice are limited. For this reason persons
accompanying accepted applicants are considered as regular participants with the same
benefits and duties: they are requested to pay a full fee and to wear the EMCSC badge.
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Special cases (children, accompanying nurse, etc.) should be negotiated with the Course
Directors.
Banking A bank service (Banco di Sicilia) is available at two-minute walk from EMCSC
(please, show your EMCSC badge at the bank counter to avoid bureaucracy)
General information After registration plrase read carefully: (1) the material in the
folder concerning the regulations of the EMCSC, meals, the location of restaurants working
for EMCSC, etc.; (2) the specific information about your course posted in the entrance hall of
San Rocco (location and starting time of lectures, programme, social events, etc.).
Get-together Do not miss the after-dinner get-together which is due at 9.30 p.m. on
the arrival day at the Marsala Room in San Rocco. Do your best to reach Erice before 5pm in
order to have enough time to get in touch with the environment and to have a quiet dinner.
No problem if you can reach Erice only late at night: somebody will be waiting for you at the
arrival location you entered in your Travel Form. Participants from remote areas may ask
however to arrive one day earlier, with no extra-charge provided rooms are available.
Smoking is forbidden inside all the facilities of the EMCSC (San Rocco, San Domenico,
San Francesco), including rooms.
Dress Erice is at about 800 m above sea level, on top of a mountain next to the sea.
Even in Summer evenings in Erice may be chill and, occasionally, foggy or/and windy. Do not
forget a good pull-over. Lecture rooms are inside old buildings and are agreeably fresh. On
the other hand temperature at the archeological sites as well as at the beach can be blistering
hot. Take all possible precaution: light stuff, good jogging shoes (to walk on the stones of the
archeological sites as well as on the rough pavement of Erice streets), swimming suite (beach
towels are provided by the EMCSC), sun-glasses, a good hat, etc. No formal dress is requested
in any event, banquet included.
Shopping Celebrated wines, cookies, ceramics, coral jewels and other Erice souvenirs
may be purchased in some (not all) shops with a 10% discount (just show the EMCSC badge).
Music EMCSC facilities host two old (occasionally in tune!) pianos. Participants playing
portable instruments are encouraged to bring them along (with the scores). Classic or folk
music sessions are often organized in San Rocco, especially after some glasses of Marsala.
Technical facilities Moderate xerox-copying is free. A limited number of PC’s and
internet terminals are available to participants. Free Wi-Fi access points are available on all
premises. The EMCSC is equipped with power-point facilities as well as all traditional
projectors.
EMCSC Personnel The EMCSC relies on a local staff, reduced in number but extremely
efficient, ready to solve all difficult problems which may arise (travel ticket & reservation
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changes, PC facilities, visa, medical care, police, etc.). The reference person is Mr. Pino Aceto.
For all technicalities concerning the course (travel grants, posters, transparencies, etc.) there
is a School Secretariat office at San Rocco next to the Marsala Room.
CM vs. EMCSC The EMCSC is not a village of Club Mediterraneé®. Besides planning
one or more excursions to the archeological sites and/or the beach, a long break is scheduled
between the morning and afternoon sessions to allow for contacts and discussions in the
inspiring environment of Erice. The School discourages trips to the beach during the full
working days and should not be requested to organize excursions besides the planned ones.
The success of the School relies on the full participation of all students to all sessions.
