Lagrangian Flow Network approach to an open flow model

Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this methodology to open chaotic flows, and check it with numerical results for a model open flow, namely a jet with a localized wave perturbation. We find that network nodes with high values of out-degree and of finite-time entropy in the forward-in-time direction identify the location of the chaotic saddle and its stable manifold, whereas nodes with high in-degree and backwards finite-time entropy highlight the location of the saddle and its unstable manifold. The cyclic clustering coefficient, associated to the presence of periodic orbits, takes non-vanishing values at the location of the saddle itself.Comment: 7 pages, 3 figures. To appear in European Physical Journal Special Topics, Topical Issue on "Recent Advances in Nonlinear Dynamics and Complex Structures: Fundamentals and Applications

Energy consumption and cooperation for optimal sensing

The reliable detection of environmental molecules in the presence of noise is an important cellular function, yet the underlying computational mechanisms are not well understood. We introduce a model of two interacting sensors which allows for the principled exploration of signal statistics, cooperation strategies and the role of energy consumption in optimal sensing, quantified through the mutual information between the signal and the sensors. Here we report that in general the optimal sensing strategy depends both on the noise level and the statistics of the signals. For joint, correlated signals, energy consuming (nonequilibrium), asymmetric couplings result in maximum information gain in the low-noise, high-signal-correlation limit. Surprisingly we also find that energy consumption is not always required for optimal sensing. We generalise our model to incorporate time integration of the sensor state by a population of readout molecules, and demonstrate that sensor interaction and energy consumption remain important for optimal sensing.Comment: 9 pages, 5 figures, Forthcoming in Nature Communication

Spectral signature of nonequilibrium conditions

The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time evolution in various ways. Here we review the dynamics of stochastic systems from the viewpoint of nonequilibrium thermodynamics. We explore the effect of external thermodynamic forces on the possible dynamical regimes and show that the time evolution can become intrinsically different under nonequilibrium conditions. For example, nonequilibrium systems with real dynamical components are similar to equilibrium ones when their state space dimension N < 5, but this equivalence is lost in higher dimensions. Out of equilibrium systems thus present new dynamical behaviors with respect to their equilibrium counterpart. We also study the dynamical modes of generalized, non-stochastic evolution operators such as those arising in counting statistics