In this CRC colloquium we're happy to welcome:

Scott McKinley (Tulane Univ., New Orleans, LA, USA)

Title: Parameter inference in the context of the generalized Langevin equation

The range of observed movement of individual microparticles (viruses, bacteria, organelles, etc) in biological fluids (mucus, cytoplasm, and interstitial fluid) poses a host of mathematical and statistical challenges. In contrast to the assumptions defining Brownian motion, which is the default model for random particle movement in viscous fluids, experimental data has revealed significant memory effects, persistent state-switching, and irregular geometric constraints. After taking a brief look at "what's out there in the data," we will focus on one model, the generalized Langevin equation, looking both at its mathematical properties and the challenges associated with statistical inference and translating particle properties into information about their fluid environment.

References:

- S. A. McKinley and H. D. Nguyen, SIAM J. Math. Anal. 50:5119, 2018.

- C. Hohenegger and S. A. McKinley, SIAM J. Appl. Math. 78:2200, 2018.

- S. A. McKinley and H. D. Nguyen, J. Fourier Anal. Appl. 28:13, 2022.

Aleksei Chechkin (U Potsdam/Kharkiv Univ.)

Title: Tempering, bimodality and heterogeneity in fractional Brownian motion

I will make a short overview of three recent studies in the theory of fractional Brownian motion (FBM). First, I will discuss different models of tempered (truncated) FBM leading to either normal diffusion or stationary state in the long-time limit. Second, I will tell about unusual shapes of stationary probability densities of FBM in external super- and subharmonic potentials and striking analogy with the confined Levy flights. Finally, very recent results on FBM with random Hurst exponent will be presented.

Aljaz Godec (MPI for Multidisciplinary Sciences, Göttingen)

Title: Towards a sample path-based statistical mechanics

Single-molecule and particle-tracking experiments interrogate physical observables along individual trajectories. These observables often correspond to lower-dimensional projections of high-dimensional dynamics or a spatially coarse-grained (i.e. "binned") version thereof, and the experiments are typically analyzed by time-averaging along individual traces. It has long been known that projections that couple to slow hidden degrees of freedom give rise to memory in the observed dynamics. However, we are only beginning to understand the implications of projections and spatial coarse graining for thermodynamics, in particular in systems driven far from thermodynamic equilibrium. I will review our recent efforts on how to describe and understand fluctuations and dissipation on the basis of path-based observables in systems driven out of equilibrium.

References:

- Cai Dieball & Aljaz Godec, Phys. Rev. Lett., article in press (2023); https://arxiv.org/abs/2208.06402

- Cai Dieball & Aljaz Godec, Phys. Rev. Lett. 129, 140601 (2022)

- Cai Dieball & Aljaz Godec, Phys. Rev. Research 4, 033243 (2022)

- Cai Dieball & Aljaz Godec, J. Phys. A: Math. Theor. 55, 475001 (2022)