Metastable transitions in time-dependent driven disordered systems: From deformable structures in random media to adaptive walks in random fitness landscapes

• Applicant: Dr. Muhittin Mungan
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 398962893

The properties of deformable structures interacting with a random medium are governed by the interplay between the deformation energy cost and the gain in energy by adjusting to the disordered environment. This interplay gives rise to a complex energy landscape, consisting of a large number of metastable states which can be formed and destroyed by varying external fields. As a result, such systems exhibit glassy behavior, dynamically critical transitions, as well as memory-effects and hysteresis. The theoretical description of deformable structures also bears similarities to the adaptive evolution of a biological population under the influence of mutation and selection: the evolution of the population is governed by a fitness landscape that encodes the interactions between genetic loci and their evolutionary fitness. The fitness landscape and energy landscape play similar roles in governing the dynamics of these systems. The goal of this project is to gain a better understanding of the dynamics on time-varying energy and fitness landscapes. In particular, we aim at obtaining rigorous results for: (A) the response of a sheared amorphous solid to athermal time-periodic forcing, by determining the possible metastable transitions, hysteresis properties, the structure of asymptotic states and whether these can retain a memory of the forcing. The second component of this project, (B), concerns the adaptive dynamics of a biological population in time-varying fitness landscapes. By making use of analogous ideas and results from thedynamics on energy landscapes, the emphasis will be on time-varying fitness landscapes created by treatment protocols such as drug-cycling. We propose to study the conditions under which the genotype of a bacterial population can be steered by the forcing into an asymptotic state of low fitness and hence low drug resistance. We intend to apply theoretical methods of non-equilibrium statistical physics, probability theory and mathematical statistics. Numerical simulations, both as an exploratory aid as well as for verification, will also be a part of the project.

• DFG Programme: Research Grants
• International Connection: Israel
• Cooperation Partner: Professor Dr. Ido Regev