Video https://drive.google.com/file/d/1krUY0f5wYT18sImWS_NGfvPNE8dg4Du1/view?usp=sharing
Video https://drive.google.com/file/d/1knIDMVd_sNoEFP7hlbCH-eNpRBG_lAhy/view?usp=sharing
Video https://drive.google.com/file/d/1kebJ_i5nMGkrEmmspMCKmDfH7DISSyzV/view?usp=sharing
Video https://drive.google.com/file/d/1vHCKG4Ip_6eEvNd7m5bhZ84jrOsS7nCf/view?usp=sharing
Title: Miraculous Hydrodynamics
Our movies illustrate phenomena of hydrodynamics arising as limits of large systems of "atomic" particles. Deriving the laws of fluid motion at a macroscopic level from first principles at microscopic (particle) level is a major challenge of statistical physics. Plainly said: Understand the motion of waves and whirls of a river or around a flying airplane, explained from laws of physics acting at the scale of molecules.
We illustrate these phenomena by simulation of a simplified model, consisting of four types of particles moving on a (microscopic) square grid. Blue, Red, Yellow and Green particles jump to North or East, South or West, North or West, and South or East, respectively. However, they interact: At any time at most one particle can occupy any site. Whenever a particle jumps, it forces the particle occupying the target site to swap position. Boundaries are periodic: particles exiting the container enter on the opposite side.
We see the apparently macroscopic (box size 500x500, far from ∞x∞!) fluid motion starting from various non-equilibrium initial states. We see waves, whirls, shocks and rarefactions, various eye-catching patterns arising from these oversimplified elementary rules. Imagine how rich in phenomena, patterns and beauty is the real physical world!
Balázs Maga is a young researcher at the Alfréd Rényi Institute of Mathematics in Budapest, where his work spans a range of topics in mathematics, e.g., analysis, dynamical systems, combinatorics. He completed his PhD on fractal geometry in 2024. Alongside his theoretical research, Balázs has a strong interest in artificial intelligence. He has gained hands-on experience in the field, particularly in computer vision and medical imaging, through his own business ventures.
Bálint Tóth is a research professor at the Alfréd Rényi Institute of Mathematics Budapest and Chair of Probability at the School of Mathematics, University of Bristol. His research focuses on problems of probability theory and stochastic processes motivated by equilibrium and non-equilibrium statistical physics. E.g., random walks and diffusions with long memory, scaling limits of interacting particle systems, hydrodynamic limits, stochastic phenomena arising in deterministic dynamics. He served as chief-editor of multiple leading journals of probability theory. He is a corresponding member of the Hungarian Academy of Science.