I have studied (mainly using computer simulations ;P) a broad range of non-equilibrium systems. Below is a brief summary.
High-performance Stochastic Partial Differential Equation Solvers for Mesoscale Systems
One major challenge problem in computational science is the description of the mesoscale (i.e. length scales of typically 1 micro-meter). These are physical systems which are too large to be effectively simulated by an atomistic description (due to the extreme number of atoms), yet they are too small to be accurately described by existing coarse-grained continuum theories. This leaves many important questions in the fields of microfluidics, nano-technology, and biology open. Most theories for mesoscale systems are governed by stochastic partial differential equations (cf. Fluctuating Hydrodynamics). Here we use AMReX, which is a powerful tool enabling us to construct finite volume schemes for solving partial differential equations. Our algorithms are designed with the next generation of supercomputer in mind.
The tools used to generate the data for this study are available here
- Weiqun Zhang, Ann Almgren, Vince Beckner, John Bell, Johannes Blaschke, Cy Chan, Marcus Day, Brian Friesen, Kevin Gott, Daniel Graves, Max P. Katz, Andrew Myers, Tan Nguyen, Andrew Nonaka, Michele Rosso, Samuel Williams, Michael Zingale. AMReX: a framework for block-structured adaptive mesh refinement. Journal of Open Source Software, 4, 1370, 2019.
Statistical Physics of Hydrodynamically and Chemically Interacting Microswimmers
The collective dynamics of microorganisms and artificial microswimmers is relevant both to real world applications, as well as for posing fundamental questions in non-equilibrium statistical physics. A striking feature of their collective behavior is that for sufficiently strong self-propulsion, they phase-separate into a dense cluster coexisting with a low-density gas-like surrounding. Our research demonstrates that hydrodynamics is essential to the concept of motility-induced phase separation. Here we show that in the mechanical equilibrium a previously neglected hydrodynamic pressure has to be added. Surprisingly the phase coexistence region (binodal) is shifted by the overall mean density. To our knowledge, this is the first example of a phase-separating system where phase coexistence depends on total number of particles. Furthermore, using fully 3-dimensional hydrodynamics simulations, we explore the interplay of sedimentation and activity-induced convection.
Felix Ruehle, Johannes Blaschke, Jan-Timm Kuhr, and Holger Stark. Gravity-induced dynamics of microswimmers in wall proximity. New Journal of Physics, 20, 025003, 2018.
Jan-Timm Kuhr, Johannes Blaschke, Felix Ruehle, and Holger Stark. Collective sedimentation of squirmers under gravity. Soft Matter, 13 7548-7555, 2017.
Johannes Blaschke, Maurice Maurer, Karthik Menon, Andreas Zoettl, and Holger Stark. Phase separation and coexistence of hydrodynamically interacting microswimmers. Soft Matter, 12, 9821-9831, 2016.
Statistical Physics of Brownian Motors far from Equilibrium
Brownian motors are fascinating to statistical physics as they are capable of rectifying fluctuations from a noisy environment. Most studies so far have considered Brownian motors out of equilibrium coupled to an environment which is itself in equilibrium. We explore the impact of the environment deviating from equilibrium for a 1-dimensional Brownian motor for the following cases: 1) an energy (heat) current flows through the bath; 2) the bath is homogeneously externally driven. We find that deviating from a Maxwellian gas reveals a rich range of motor behavior. We show that rectification can occur due to a flow of entropy alone, i.e. rectification occurs even if there is no energy flow to the motor. This constitutes a qualitatively different class of Brownian motor, an Entropic motor.
- Johannes Blaschke and Juergen Vollmer. Granular Brownian motors: Role of gas anisotropy and inelasticity. Phys. Rev. E, 87, 040201(R), 2013
Nucleation Dynamics of Droplets and Coarsening on Surfaces
The pattern of small droplets formed when liquid vapor condenses on a substrate is also known as a Breath Figure. Breath figures are an essential tool for understanding the mass and heat transport of systems exhibiting condensation. A model introducing a growth process of the droplets (i.e. touching droplets coalesce), as well as two length scales: 1) a smallest droplet size (nucleation); 2) and a largest droplet size (dripping), was analyzed numerically. The scaling theory describing the droplet size distribution has been extended to account for these new length scales.
The tool used to generate the data for this study is available here.
- Johannes Blaschke, Tobias Lapp, Bjoern Hof, and Juergen Vollmer. Breath Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets. Phys. Rev. Lett., 109, 068701, 2012.