Curriculum Vitae - APC - Université Paris Diderot-Paris 7

compares to the typical width of the channels, or to the distance between the obstacles. Indeed, the
particles then behave as “mobile clogs”, which locally modify the network conductivity, thereby
inducing large-scale flow disturbances. Similarly, cutting a single wire in an electrical network
would results in a global redistribution of the electric current, though the electrical conductivity is
only modified locally. In addition, we know that cutting a finite fraction of the wires in an
electrical network is enough to destroy it. Going back to the fluidic problem, this means that a
finite fraction of clogs is enough obstruct the network. However, what makes the problem much
more challenging in the fluidic context, is that the particles we want to transport are themselves
responsible for the obstruction. More precisely, the local (partial) clogging makes the particletransport
problem, nonlinear and nonlocal, as the local particle current depends a priori on the
position of all the other particles in the network. So far, the description of the transition from a
stationary flowing state to a jammed state where the particles remain trapped in the network is an
open problem (see also the state of the art section III). Precisely we purpose to provide a first
quantitative understanding of this problem, which is relevant for all the afore-mentioned examples
(Filtration, enhance oil recovery, blood microflows,…).
Traffic of self-propelled particles: collective motion and beyond
In the case of self-propelled particles, the traffic dynamics is already highly non-trivial even for
small particles. Self-propelled particles can be basically considered as random walkers having a
finite persistence length. The understanding of the diffusion of non-interacting particles in
heterogeneous media, and more specifically in disordered media, has drawn much attention over
the last 30 years. This canonical statistical mechanics problem is a paradigm both for transport
problems but also for the relaxation of disordered materials in their conformational space, see e.g.
[5]. The description of the collective traffic dynamics of motile agents in disordered fluidic
networks goes beyond this framework. It indeed requires to take into account the contact, and, or
hydrodynamic interactions between the particles, thereby making the theoretical description of
these systems utterly challenging. Again, this situation is relevant to all the traffic phenomena
discussed in the introduction. In fact, most of the studies on the collective behavior of selfpropelled
particles have hitherto focused on the emergence of collective behavior such as the
formation of large-scale cluster undergoing coherent motion in homogeneous media, such as the
one observed in fish schools, bird flocks, and bacterial swarms [12,14]. How can these results be
extended to the traffic in heterogeneous media such as disordered obstacle networks or random
channel networks? Despite the question sounds very natural when considering all the examples
given in the introduction (vehicle traffic in urban networks, contamination of soils and
cytoplasmic streaming, …), to the best of our knowledge, these questions have never been
addressed from a physics perspective.
Position of the project
In order to uncover the generic features of these two classes of traffic processes, we will
systematically combine concepts and tools from soft-condensed matter, statistical mechanics
and hydrodynamics. The project is in essence a fundamental research project. It will mainly
contribute to knowledge development. Also, more direct applications of our research must not
be eluded. To inspire and guide our questioning, we will definitely take advantage of our
current collaborations with one of our industrial sponsor, TOTAL, which has today a crucial
need of a physical input to achieve controlled and efficient enhance oil recovery in the highly
strategic heavy-oil fields. Finally, we hope to be capable of making statements relevant to
many research areas, possibly bringing new light to fields outside of fluid mechanics and softcondensed
matter.