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Cooperative surmounting of bottlenecks
The physics of activated escape of objects out of a metastable state plays a
key role in diverse scientific areas involving chemical kinetics, diffusion and
dislocation motion in solids, nucleation, electrical transport, motion of flux
lines superconductors, charge density waves, and transport processes of
macromolecules, to name but a few. The underlying activated processes present
the multidimensional extension of the Kramers problem of a single Brownian
particle. In comparison to the latter case, however, the dynamics ensuing from
the interactions of many coupled units can lead to intriguing novel phenomena
that are not present when only a single degree of freedom is involved. In this
review we report on a variety of such phenomena that are exhibited by systems
consisting of chains of interacting units in the presence of potential
barriers.
In the first part we consider recent developments in the case of a
deterministic dynamics driving cooperative escape processes of coupled
nonlinear units out of metastable states. The ability of chains of coupled
units to undergo spontaneous conformational transitions can lead to a
self-organised escape. The mechanism at work is that the energies of the units
become re-arranged, while keeping the total energy conserved, in forming
localised energy modes that in turn trigger the cooperative escape. We present
scenarios of significantly enhanced noise-free escape rates if compared to the
noise-assisted case.
The second part deals with the collective directed transport of systems of
interacting particles overcoming energetic barriers in periodic potential
landscapes. Escape processes in both time-homogeneous and time-dependent driven
systems are considered for the emergence of directed motion. It is shown that
ballistic channels immersed in the associated high-dimensional phase space are
the source for the directed long-range transport
Surmounting collectively oscillating bottlenecks
We study the collective escape dynamics of a chain of coupled, weakly damped
nonlinear oscillators from a metastable state over a barrier when driven by a
thermal heat bath in combination with a weak, globally acting periodic
perturbation. Optimal parameter choices are identified that lead to a drastic
enhancement of escape rates as compared to a pure noise-assisted situation. We
elucidate the speed-up of escape in the driven Langevin dynamics by showing
that the time-periodic external field in combination with the thermal
fluctuations triggers an instability mechanism of the stationary homogeneous
lattice state of the system. Perturbations of the latter provided by incoherent
thermal fluctuations grow because of a parametric resonance, leading to the
formation of spatially localized modes (LMs). Remarkably, the LMs persist in
spite of continuously impacting thermal noise. The average escape time assumes
a distinct minimum by either tuning the coupling strength and/or the driving
frequency. This weak ac-driven assisted escape in turn implies a giant speed of
the activation rate of such thermally driven coupled nonlinear oscillator
chains
Microscopic insights into pedestrian motion through a bottleneck, resolving spatial and temporal variations
The motion of pedestrians is subject to a wide range of influences and
exhibits a rich phenomenology. To enable precise measurement of the density and
velocity we use an alternative definition using Voronoi diagrams which exhibits
smaller fluctuations than the standard definitions. This method permits
examination on scales smaller than the pedestrians. We use this method to
investigate the spatial and temporal variation of the observables at
bottlenecks. Experiments were performed with 180 test subjects and a wide range
of bottleneck parameters. The anomalous flow through short bottlenecks and
non-stationary states present with narrow bottlenecks are analysed
Restricted trees: simplifying networks with bottlenecks
Suppose N is a phylogenetic network indicating a complicated relationship
among individuals and taxa. Often of interest is a much simpler network, for
example, a species tree T, that summarizes the most fundamental relationships.
The meaning of a species tree is made more complicated by the recent discovery
of the importance of hybridizations and lateral gene transfers. Hence it is
desirable to describe uniform well-defined procedures that yield a tree given a
network N. A useful tool toward this end is a connected surjective digraph
(CSD) map f from N to N' where N' is generally a much simpler network than N. A
set W of vertices in N is "restricted" if there is at most one vertex from
which there is an arc into W, thus yielding a bottleneck in N. A CSD map f from
N to N' is "restricted" if the inverse image of each vertex in N' is restricted
in N. This paper describes a uniform procedure that, given a network N, yields
a well-defined tree called the "restricted tree" of N. There is a restricted
CSD map from N to the restricted tree. Many relationships in the tree can be
proved to appear also in N.Comment: 17 pages, 2 figure
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Big bottlenecks in cardiovascular tissue engineering.
Although tissue engineering using human-induced pluripotent stem cells is a promising approach for treatment of cardiovascular diseases, some limiting factors include the survival, electrical integration, maturity, scalability, and immune response of three-dimensional (3D) engineered tissues. Here we discuss these important roadblocks facing the tissue engineering field and suggest potential approaches to overcome these challenges
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