We shall discuss on some variants of the TASEP, motivated by modeling
of queues and biological applications. In some simple cases, one can
easily construct exact (unnormalized) stationary measures by slightly
arranging known matrix product form in the standard open boundary
conditions. By arguing convergency of these stationary measures, we
can determine dynamical phase transition lines separating between
convergent and divergent phases. With helps of Monte Carlo
simulations, we also consider further extended models with e.g.
Langmuir kinetics.

Abstract:

The competition between aggregation and fragmentation can lead to interesting phases. For instance, in a lattice model of diffusing masses which coalesce when they meet, and chip off small bits as they move along, there is a phase transition to a state with a power-law mass distribution plus a single infinite aggregate. Motivated by the problem of protein transport through the Golgi organelle, we study the corresponding open system with mass injection and output at the boundaries, and find a phase transition to an interesting state with strong intermittency in time. On including the feature of chemical processing we arrive at a minimalist model for proteins moving in the Golgi. We propose new quantitative measures that can distinguish between the two contending models (vesicular transport and cisternal maturation) for protein transport through the organelle.

References:

[1] Multispecies model with interconversion, chipping, and injection
H. Sachdeva, M. Barma and Madan Rao, Phys. Rev. E 84, 031106 (2011).
[2] Condensation and Intermittency in an Open-Boundary Aggregation-Fragmentation Model
H . Sachdeva, M. Barma and Madan Rao, Phys. Rev. Lett. 110, 150601 (2013).
[3] Analytical Study of Giant Fluctuations and Temporal Intermittency
H. Sachdeva and M. Barma, J. Stat. Phys. 154, 950 (2014).
[4] Physical mechanisms underlying de nouvo biogenesis of Golgi cisterna H. Sachdeva, M. Barma and Madan Rao

Abstract:

The Totally Asymmetric Simple Exclusion Model (TASEP) is a paradigmatic model for understanding the rich world of low-dimensional non-equilibrium phenomena. It was first introduced to model kinetics of protein synthesis, but later found a number of applications in biological transport, vehicular traffic, forced motion of colloids in narrow channels, etc.
Here we report on some novel features of the stationary phases of TASEP on long open chains with a shortcut in the bulk, which model the motion of molecular motors along twisted protofilaments. In such cases the molecular motors can jump with some probability between sites very distant along the backbone but close in real space (shortcuts). We have shown that crowding phenomena (shock phases), which may be responsible for some human diseases [1], exist under certain conditions in the presence of both zero-length [2] and finite-length [3] shortcuts. The theoretical classification of all the possible stationary phases of the network is based on our Effective Rates Approximation [4]. When the whole track carries the maximum current, the particle density profile and the nearest-neighbor correlations in the shunted segment are well described by the theory of completely delocalized domain walls between the low- and high-density phases which occur under that current [5]. It is shown that in the case of a zero-length shortcut, the shock phase exists when the effective injection and ejection rates for the shunted segment are equal and obey a cubic equation with coefficients linearly depending on the probability of choosing the shortcut. In the case of a shortcut with arbitrary length and any values of the external rates in the domain of the maximum current phase, there always exists a position of the shortcut when the shunted segment is in the shock phase. At that, the current through the longer shunted segment is higher than the one through the shortcut.

References:

[1] E. Pronina and A. B. Kolomeisky, J. Stat. Mech.: Theor. Exp. 07, P07010 (2005). [2] N. Bunzarova, N. Pesheva, and J. Brankov, Phys. Rev. E 89, 032125 (2014). [3] N.Zh. Bunzarova, N.C. Pesheva, and J.G. Brankov, Physica A 438, 645 (2015).
[4] J. Brankov, N. Pesheva, and N. Bunzarova, Phys. Rev. E 69, 066128 (2004). [5] A.B. Kolomeisky, G.M. Schütz, E.B. Kolomeisky, and J.P. Straley, J. Phys. A 31, 6911 (1998).

Abstract:

I will discuss the normalisation of the stationary state of the multi-species asymmetric exclusion process (ASEP) in relation to the theory of symmetric polynomials. On a ring the normalisation can be shown to be a specialisation of a Macdonald polynomial while for open boundary conditions it is given by a specialisation of a Koornwinder polynomial. I will also discuss how the matrix product method for multi-species ASEP leads to new expressions for Macdonald polynomials and generalisations.

Abstract:

I will show how problems coming from the study of the dynamics of Ising
spins,either in one or two dimensions, naturally lead to questions, solved or
unsolved, on the symmetric or asymmetric exclusion process.

Abstract:

The dynamics of stochastic classical particle systems, when a
rare event takes place in them, is usually very complicated. In this talk
we investigate the interactions in the effective dynamics of an exactly
solvable model at an atypical time-integrated current.

Abstract:

In this talk, I will present details of our recent car-following experiments in a platoon of 25 cars and 51 cars. We reveal that (i) the spacing between a leading car and a following car can change significantly even though the speeds of the two cars are essentially constant and the velocity difference is very small; (ii) the platoon length (hence the average spacing within a platoon) might be significantly different even if the average velocity of the platoon is essentially the same. This feature clearly contradicts
the fundamental assumption that there is a unique relationship between vehicle speed and its spacing in traditional car-following models. We also report that oscillations grow along the platoon in a concave way. Simulations show that by removing the undamental notion in the traditional car-following models and allowing the traffic state to span a two-dimensional region in velocity-spacing plane, the growth pattern of disturbances has changed qualitatively and becomes qualitatively or even quantitatively in consistent
with that observed in the experiment.

Abstract:

All living organisms rely on ribosomes, the nanomachines that synthesize proteins by translating the codon sequences of mRNAs into proteins. During the elongation cycle of protein synthesis, the ribosometranslates one codon after another by initial binding a ternary complex, decoding of this complex, full accommodation into the A site of the ribosome followed by a translocation step that moves the ribosome to the next codon. The talk describes a recently introduced Markov model that describes all of these ribosomal states and transitions and has been validated by three independent sets of in-vivo data.

References:

[1] Sophia Rudorf and Reinhard Lipowsky, PLoS Comp. Biol. 10, e1003909 (2014)
[2] PLoS ONE 10, e013494 (2015)

Abstract:

I analyse far from equilibrium transport of a periodically driven inertial
Brownian particle moving in a periodic potential. The mean square deviation
of the particle position from its average may involve three distinct
intermediate, although extended diffusive regimes: initially as
superdiffusion, followed by subdiffusion and finally, normal diffusion in
the asymptotic long time limit. Even though these anomalies are transient
effects, their lifetime can be many, many orders of magnitude longer than
the characteristic time scale of the setup and turns out to be
extraordinarily sensitive to the system parameters like temperature or the
potential asymmetry. I show that mechanisms of diffusion anomalies is
related to ergodicity of the system, symmetry breaking of the periodic
potential and ultraslow relaxation of the particle velocity towards its
steady state. Similar sequences of the diffusive behaviours could be
detected in various systems including, among others, colloidal particles
in random potentials, glass forming liquids and granular gases.

Abstract:

We study miniaturized noncontact rack and pinion composed of a corrugated plate and a corrugated cylinder intermeshed via the lateral Casimir force. The axle of the pinion is subject to Casimir torque, frictional torque, load torque, and random Gaussian torque. The interplay of the friction loss and the external drive allows the system to reach the steady state. We show that the Casimir machines can be used to measure Casimir force, rectify deterministic motion, harvest energy from noise, and sense displacements and vibrations.

Abstract:

Actuated and autocatalytic colloids constitute systems that are
intrinsically out of equilibrium. As a result of their dynamic
interactions, they can show a rich variety of self assembly scenarios.
The observed self assembled structures make these systems very sensitive
to external forcing, hence making actuated and active matter a fertile
ground to explore and develop mechanically tunable materials.
In this talk I will analyze the basic physical mechanisms that control the
collective behavior of two kinds of colloidal particles that move in a
liquid medium. On the one hand, confined magnetic colloids can rectify
their motion when actuated with a rotating magnetic field, acting as a
ydrodynamic conveyor belt. Self assembled chains of rotors propel faster
than individual ones, until reaching a saturation speed at distances where
induced-flow additivity vanishes. On the other hand, the development of
Janus colloids has opened the possibility to create synthetic microrobots
that can move due to the chemical reactions they catalyze on their
heterogeneous surfaces. The motion of chemically powered colloids is
intricate because the chemically active colloids perturb the spatial
distribution of the chemical species and also the state of motion of the
solvent. As a result, suspensions of chemically active colloids are
characterized by long range, non-equilibrium interactions. These dynamic
interactions have a strong impact in the collective behavior of these
suspensions. I will describe the analogies and specificities in the
hydrodynamic coupling that characterize these two types of systems and the
different structures they spontaneously form.

References:

[1] B. Liebchen, D. Marenduzzo, I. Pagonabarraga, M.E. Cates, Phys. Rev.
Lett. 115, 258301 (2015)
[2] F. Martinez-Pedrer, A. Ortiz-Ambriz, I. Pagonabarraga, P. Tierno,
Phys. Rev. Lett. 115, 138301 (2015)
[3] A. Scagliarini, I. Pagonabarraga, submitted

Abstract:

The asymmetric simple exclusion process (ASEP) is a prototypical model for
stochastic transport phenomena, but it can also be regarded as a model for random
growth processes. In fact, recent years have witnessed a series of breakthroughs
about universal fluctuation properties of such growth processes, known by the name
of the Kardar-Parisi-Zhang (KPZ) universality class, and ASEP has played central
roles in it. In this talk, I will review some of the central exact results from ASEP
and discuss their consequences for random growth processes, which also unveiled
connections to the wealth of different problems, such as random matrices, directed
polymer, and so on [1]. I will also present our experimental observations of growing
interfaces in liquid-crystal turbulence [2]. This experiment not only serves as a
test of universality of the theoretical results, but provides quantitative hints for
some statistical quantities, which remain hitherto unsolved for ASEP and other
related models.

References:

[1] For reviews, see, e.g., T. Kriecherbauer and J. Krug, J. Phys. A 43, 403001
(2010); I. Corwin, Random Matrices Theory Appl. 1, 1130001 (2012); T. Sasamoto,
Prog. Theor. Exp. Phys. (2016), 022A01
[2] K. A. Takeuchi and M. Sano, Phys. Rev. Lett. 104, 230601 (2010); K. A. Takeuchi
et al., Sci. Rep. 1, 34 (2011); K. A. Takeuchi and M. Sano, J. Stat. Phys. 147, 853
(2012).

Title of Lectures:

Abstract:

We discuss some interesting outcomes of the competition between aggregation and fragmentation. In a simple lattice model, mean field theory predicts an interesting phase transition to a “condensate state” in which a single site holds a finite fraction of the mass. This is confirmed by simulations as well as an exact determination of the phase boundary. In the corresponding open system with input and output at the edges, the system is found to show giant, fluctuations of the mass. The time-dependent correlation functions are intermittent, as opposed to self-similar, established both by simulations and an exact calculation for a limiting case in 1D. Possible applications and extensions to situations involving traffic (including protein transport through the Golgi organelle) will be discussed.

Abstract:

In a class of driven, nonequilibrium systems, fluctuations are anomalously strong but coexist with long-range order, leading to fluctuation-dominated phase ordering (FDPO). States showing FDPO have been found in a variety of models: passive scalar particles advected by fluctuating surfaces; protein clustering on cellular membranes; granular media with velocity-dependent restitution. There is also evidence of FDPO in experiments on vibrated rods.
This lecture will introduce FDPO through a simple model of particles sliding under gravity on a fluctuating surface, and a related coarse-grained depth model. Under coarsening, the two-point correlation function shows scaling, but interestingly, the corresponding scaling function shows a singularity, implying the breakdown of the Porod Law in such systems.
Further, an infinite set of one-point functions is introduced to capture the continual breakup and joining of macroscopic ordered regions in time. Finally, we discuss hints of an intriguing connection between FDPO and systems with quenched disorder.

Abstract:

Traffic flow complexity comes from both car-following and lane-changing behavior. In microscopic traffic flow research,
one usually first establishes and studies the car-following models, then introduces lane changing behavior and other
measurements into the car-following models to deal with multilane traffic flow, mixed traffic flow, on-ramps, off-ramps,
etc. Therefore, car-following models play a very important role in traffic flow studies. In this lecture, I will introduce
some classical car-following models such as GM models, Newell model, optimal velocity model, intelligent driver model
as well as some recent models, such as Kerner-Klenov model, 2D-intelligent driver model, insensitivity model.

Abstract:

In
this
talk,
I
will
introduce
our
recent
works
on
traffic
flow
simulation
in a
Manhattan-like
urban
system.
In
this
model,
the
origin–destination
trips
and
traffic
lights
have
been
considered.
The
advanced
traffic
information
system
has
been
introduced.
The
probabilistic
feature
of
traffic
breakdown
to
global
gridlock
has
been
observed.
An
index
"Network
Operation
Reliability"
has
been
proposed.
A
simple
adaptive
traffic
light
strategy
has
been
proposed.
It
has
been
shown
that
via
choosing
proper
parameters,
the
adaptive
traffic
signals
are
able
to
remarkably
enhance
the
Network
Operation
Reliability.