The study of the behavior of a driven tracer in crowded environments plays a central role in several fields, such as active microrheology experiments in complex fluids and general transport phenomena in biological systems. In particular, interesting effects can be observed in the nonlinear response regime, where anomalous behaviors can occur. In this talk, I will discuss some analytical approaches in the context of lattice gases, where the driven tracer interacts with an environment of mobile hardcore obstacles. I will focus on the interesting phenomenon of negative differential mobility, i.e. a nonmonotonic behavior of the force-velocity relation of the tracer, which is controlled by both the density and diffusion time scale of the obstacles.

We study a one-dimensional chain of masses connected by harmonic springs and subject to dry friction. The problem at the heart of our study is whether, in this sytem, the statistical properties of the configurations explored by an athermal driving mechanism can be reproduced by an effective equilibrium theory. In this seminar I present an effective theory for the harmonic chain with friction which can be exactly solved using transfer matrices and I compare its predictions with the results from numerical simulations.

Determining correlations among variables starting from some observations is a common problem in statistics. In these cases, one deals with some estimators of population correlation matrices, which are affected by finite sampling effects. One of the most common techniques generally used for this kind of problems is the principal component analysis, where one usually retains only the components corresponding to larger eigenvalues of sample correlation matrices, considered as the most informative. Actually, what is usually neglected in this procedure (namel! y the eigenvectors associated to smaller eigenvalues) is not just related to the sampling noise. Indeed, using a combination of random matrix and information-theoretic tools, I will show that all the eigenvectors of sample correlation matrices are informative about the principal components (namely, the eigenvectors associated to large eigenvalues) of the population correlation matrix. This extra information can be used in order to efficiently improve standard data cleaning procedures.

- Set ALLOWTOPICCHANGE = AndreaPuglisi

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Topic revision: r1 - 2015-06-05 - AndreaPuglisi

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