83 research outputs found
Modelling chemotaxis of microswimmers: from individual to collective behavior
We discuss recent progress in the theoretical description of chemotaxis by
coupling the diffusion equation of a chemical species to equations describing
the motion of sensing microorganisms. In particular, we discuss models for
autochemotaxis of a single microorganism which senses its own secretion leading
to phenomena such as self-localization and self-avoidance. For two
heterogeneous particles, chemotactic coupling can lead to predator-prey
behavior including chase and escape phenomena, and to the formation of active
molecules, where motility spontaneously emerges when the particles approach
each other. We close this review with some remarks on the collective behavior
of many particles where chemotactic coupling induces patterns involving
clusters, spirals or traveling waves.Comment: to appear as a contribution to the book "Chemical kinetics beyond the
textbook
Interaction-induced current-reversals in driven lattices
We demonstrate that long-range interactions can cause, as time evolves,
consecutive reversals of directed currents for dilute ensembles of particles in
driven lattices. These current-reversals are based on a general mechanism which
leads to an interaction-induced accumulation of particles in the regular
regions of the underlying single-particle phase space and to a synchronized
single-particle motion as well as an enhanced efficiency of Hamiltonian
ratchets.Comment: 5 pages, 5 figure
Which Interactions Dominate in Active Colloids?
Despite a mounting evidence that the same gradients which active colloids use
for swimming, induce important cross-interactions (phoretic interaction), they
are still ignored in most many-body descriptions, perhaps to avoid complexity
and a zoo of unknown parameters. Here we derive a simple model, which reduces
phoretic far-field interactions to a pair-interaction whose strength is mainly
controlled by one genuine parameter (swimming speed). The model suggests that
phoretic interactions are generically important for autophoretic colloids
(unless effective screening of the phoretic fields is strong) and should
dominate over hydrodynamic interactions for the typical case of half-coating
and moderately nonuniform surface mobilities. Unlike standard minimal models,
but in accordance with canonical experiments, our model generically predicts
dynamic clustering in active colloids at low density. This suggests that
dynamic clustering can emerge from the interplay of screened phoretic
attractions and active diffusion.Comment: v2,v3 discussion improved, emphasized model limitations; v4 small
changes throughout, notation slightly changed, typos corrected, figure
update
Formation of density waves via interface conversion of ballistic and diffusive motion
We develop a mechanism for the controlled conversion of ballistic to
diffusive motion and vice versa. This process takes place at the interfaces of
domains with different time-dependent forces in lattices of laterally
oscillating barrier potentials. As a consequence long-time transient
oscillations of the particle density are formed which can be converted to
permanent density waves by an appropriate tuning of the driving forces. The
proposed mechanism opens the perspective of an engineering of the
nonequilibrium dynamics of particles in inhomogeneously driven lattices.Comment: 5 figure
Pattern formation in chemically interacting active rotors with self-propulsion
We demonstrate that active rotations in chemically signalling particles, such as autochemotactic close to walls, create a route for pattern formation based on a nonlinear yet deterministic instability mechanism. For slow rotations, we find a transient persistence of the uniform state, followed by a sudden formation of clusters contingent on locking of the average propulsion direction by chemotaxis. These clusters coarsen, which results in phase separation into a dense and a dilute region. Faster rotations arrest phase separation leading to a global travelling wave of rotors with synchronized roto-translational motion. Our results elucidate the physics resulting from the competition of two generic paradigms in active matter, chemotaxis and active rotations, and show that the latter provides a tool to design programmable self-assembly of active matter, for example to control coarsening.Marie SkĆodowska Curie (Intra European Fellowship within Horizon 2020 (Grant ID: 654908)), Royal Society, Engineering and Physical Sciences Research Counci
Phase Synchronization in Railway Timetables
Timetable construction belongs to the most important optimization problems in
public transport. Finding optimal or near-optimal timetables under the
subsidiary conditions of minimizing travel times and other criteria is a
targeted contribution to the functioning of public transport. In addition to
efficiency (given, e.g., by minimal average travel times), a significant
feature of a timetable is its robustness against delay propagation. Here we
study the balance of efficiency and robustness in long-distance railway
timetables (in particular the current long-distance railway timetable in
Germany) from the perspective of synchronization, exploiting the fact that a
major part of the trains run nearly periodically. We find that synchronization
is highest at intermediate-sized stations. We argue that this synchronization
perspective opens a new avenue towards an understanding of railway timetables
by representing them as spatio-temporal phase patterns. Robustness and
efficiency can then be viewed as properties of this phase pattern
Designing bus transit services for routine crowd situations at large event venues
National Research Foundation (NRF) Singapore under International Research Centres in Singapore Funding Initiativ
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
The decision rule approach to optimization under uncertainty: methodology and applications
Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naĂŻvely partition or discretize the support of the random problem parameters are limited to small and medium-sized problems, or they require restrictive modeling assumptions (e.g., absence of recourse actions). In the last few decades, several solution techniques have been proposed that aim to alleviate the curse of dimensionality. Amongst these is the decision rule approach, which faithfully models the random process and instead approximates the feasible region of the decision problem. In this paper, we survey the major theoretical findings relating to this approach, and we investigate its potential in two applications areas
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