Theory and Simulations of Active Brownian Systems

• Applicant: Professor Abhinav Sharma, Ph.D.
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Biophysics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 440884972

Assemblies of active, interacting Brownian particles (ABPs) are intrinsically nonequilibrium systems constituted of particles which in addition to the Brownian thermal motion, undergo self-propulsion. These particles can respond to external conditions such as gradients in concentration of chemicals, perform controlled directed motion and even exhibit highly interesting nonequilibrium phase transition behavior. The theoretical understanding of ABPs is difficult due to the fact that in contrast to equilibrium, for which the statistical mechanics of Boltzmann and Gibbs enables the calculation of average properties, there is no analogous framework out-of-equilibrium. However, useful exact expressions exist, which enable average quantities to be calculated in the nonequilibrium system by integrating an appropriate time correlation function; the Green-Kubo formulae of linear response theory. Surprisingly, the application of the response theory and time-correlation function methods to active systems has so far received little attention. Besides providing exact analytical expressions in the linear regime, the response theory can yield systematic nonlinear approximations to explore far-from-equilibrium active systems.The goal of the proposed research is to extend the Green-Kubo methods to treat ABPs in both linear and far-from-equilibrium regime. n contrast to hydrodynamical and phenomenological theories, our approach will enable quantitive, parameter free, predictions to be made, which directly relate macroscopic observables to the underlying interparticle interactions. Using the linear respose theory, exact Green-Kubo relations will be obtained that identify the physically relevant time-correlation functions. These will then be approximated using advanced theoretical methods taken from liquid state theory: mode-coupling theory and related projection operator approaches. Our approach is not limited to the linear regime. The framework presented in this proposal allows for (1) systematic development of nonlinear approximations and (2) integration with the coarse-graining method of gradient expansion to calculate quantities which admit higher than linear order response to activity.All theoretical predictions will be benchmarked using active Brownian dynamics simulations. The Green-Kubo approach has already shed light on a key quantity entering coarse grained theories of ABPs; the density-dependent, average swim speed.However, the method is general and can be applied to address the activity dependence of other important response functions, both in the linear regime and beyond. Of particular interest are the response to space- and time-dependent activity and dynamics under Lorentz force. We note that our aim is not to develop a new general theory of ABPs but rather systematically investigate the ABPs using the response theory together with other coarse-graining techniques and numerical simulations.

• DFG Programme: Research Grants
• International Connection: Italy, Switzerland
• Cooperation Partners: Professor Joseph M. Brader, Ph.D.; Professor Dr. Umberto Marconi