LPTMC Seminars

Slimming down through frustration

In many disease, proteins aggregate into fibers. Why? One could think of molecular reasons, but here we try something more general. We propose that when particles with complex shapes aggregate, geometrical frustration builds up and fibers generically appear. Such a rule could be very useful in designing artificial self-assembling systems.

Replica Symmetry breaking for Ulam's problem

The description of complex system by the concept of Replica Symmetry Breaking (RSB) was shaped by Giorgio Parisi in the 1980s to solve the mean-field spin glass, as honored by the Nobel price in 2021. RSB has been used to analyze systems such as spin glasses, neural networks, optimization problems, or machine learning. Unfortunaley, numerically these well know RSB-exhibiting problems are difficult since only exponential-time exact algorithms are available.

Here two models are considered, directed polymers in random media and increasing subsequences, called Ulam's problem for the ground states, i.e. longest subsequences. The distributions of free energies or sequence lengths, respectively, exhibit complex large-deviation behavior, which can be numerically addressed by rare-event sampling algorithms.

Furthermore, for both models it is possible to sample exactly in perfect thermal equilibrium with polynomial-time algorithms. This means, large system sizes are accessible, in contrast to, e.g., the case of spin glasses. The results from perfect sampling of some problem disorder ensembles indicate
the presence of RSB with complex structured landscapes. Thus, the study of complex RSB behavior is conveniently accessible numerically for some models.

Finally, for partially presorting random sequences, obe obtains a transition similar to a ferromagnet-spin glass transition.

Spatiotemporal Characterization of Active Dynamics in Channels: Theory and Experiments

Swimming microorganisms often live in confined, complex environments, where they transition between bulk and near-surface dynamics. Their dynamics can be quantified in terms of first-passage statistics. In this talk, I will first consider run-and-tumble bacteria confined in a channel. Combining theoretical predictions based on a renewal framework with experimental observations of Escherichia coli, we study the statistics of the time required, after leaving one wall, to encounter either wall. I will discuss how incorporating heterogeneity in tumbling rates or non-exponential run-duration distributions affects the survival probability. In the second part of the talk, I will consider active Brownian dynamics between two walls. Using a systematic expansion, we compute first-passage properties. Exploiting Siegmund duality, we infer the corresponding spatial properties for active Brownian particles confined between hard walls and reveal a transition towards a wall-accumulated state, reminiscent of experimental observations.