Universal properties of branching random walks in confined geometries

Characterizing the occupation statistics of a radiation flow through confined geometries is key to such technological issues as nuclear reactor design and medical diagnosis. This amounts to assessing the distribution of the travelled length $\ell$ and the number of collisions $n$ performed by the underlying stochastic transport process, for which remarkably simple Cauchy-like formulas were established in the case of branching Pearson random walks with exponentially distributed jumps. In this Letter, we show that such formulas strikingly carry over to the much broader class of branching processes with arbitrary jumps, provided that scattering is isotropic and the average jump size is finite.Comment: 5 pages, 3 figure

The critical catastrophe revisited

The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole neutron population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the neutrons may display a wild patchiness (clustering). On the contrary, imposing a population control on the total population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time.Comment: 16 pages, 6 figure

The Stochastic complexity of spin models: Are pairwise models really simple?

Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g. in terms of pairwise dependences) - as in statistical learning - or because they capture the essential ingredients of a specific phenomenon - as e.g. in physics - leading to non-trivial falsifiable predictions. In information theory and Bayesian inference, the simplicity of a model is precisely quantified in the stochastic complexity, which measures the number of bits needed to encode its parameters. In order to understand how simple models look like, we study the stochastic complexity of spin models with interactions of arbitrary order. We highlight the existence of invariances with respect to bijections within the space of operators, which allow us to partition the space of all models into equivalence classes, in which models share the same complexity. We thus found that the complexity (or simplicity) of a model is not determined by the order of the interactions, but rather by their mutual arrangements. Models where statistical dependencies are localized on non-overlapping groups of few variables (and that afford predictions on independencies that are easy to falsify) are simple. On the contrary, fully connected pairwise models, which are often used in statistical learning, appear to be highly complex, because of their extended set of interactions

Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.Comment: 12 pages, 6 figure

Acid/base-triggered photophysical and chiroptical switching in a series of helicenoid compounds

International audienceA series of molecules that possess two quinolines, benzoquinolines, or phenanthrolines connected in a chiral fashion by a biaryl junction along with their water-soluble derivatives was developed and characterized. The influence of the structure on the basicity of the nitrogen atoms in two heterocycles was examined and the photophysical and chiroptical switching activity of the compounds upon protonation was studied both experimentally and computationally. The results demonstrated that changes in the electronic structure of the protonated vs. neutral species, promoting a bathochromic shift of dominant electronic transitions and alternation of their character from π-to-π* to charge-transfer-type, when additionally accompanied by the high structural flexibility of a system, leading to changes in conformational preferences upon proton binding, produce particularly pronounced modifications of the spectral properties in acidic medium. The latter combined with reversibility of the read-out make some of the molecules in this series very promising multifunctional pH probes

Intrinsically Stretchable Biphasic (Solid–Liquid) Thin Metal Films

Stretchable biphasic conductors are formed by physical vapor deposition of gallium onto an alloying metal film. The properties of the photolithography-compatible thin metal films are highlighted by low sheet resistance (0.5 Ω sq−1) and large stretchability (400%). This novel approach to deposit and pattern liquid metals enables extremely robust, multilayer and soft circuits, sensors, and actuators

Broadband optical limiting optimisation by combination of carbon nanotubes and two-photon absorbing chromophores in liquids

International audienceWe report here on the optical limiting studies performed with nanosecond laser pulses on several families of multiphoton absorbers in chloroform, with carbon nanotubes suspended in solutions. Performances of these samples are compared with those of simple multiphoton absorber solutions and carbon nanotube suspensions, and the differences observed are interpreted in terms of cumulative NLO effects and adverse aggregation phenomenon