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We point out a surprising feature of diffusion in inhomogeneous media: under suitable conditions, the rectification of the Brownian paths by a diffusivity gradient can result in initially spread tracers spontaneously concentrating. This geometric ratchet effect demonstrates that, in violation of the classical statements of the second law of (non-equilibrium) thermodynamics, self-organization can take place in thermodynamic systems at local equilibrium without heat being produced or exchanged with the environment. We stress the role of Bayesian priors in a suitable reformulation of the second law accommodating this geometric ratchet effect.
In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we fi
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from particle dyna
We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic piecewise constant forces. This system can be formally solved for any external force, providing the ratchet velocity as a n
We present a detailed analysis of the self-organization phenomenon in which the stylized facts originate from finite size effects with respect to the number of agents considered and disappear in the limit of an infinite population. By introducing the
We consider an experimentally relevant model of a geometric ratchet in which particles undergo drift and diffusive motion in a two-dimensional periodic array of obstacles, and which is used for the continuous separation of particles subject to differ