טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentRabinovich Aviv
SubjectEquations of Motion for Objects in a Medium of Active
Particles
P
DepartmentDepartment of Physics
Supervisor Professor Yariv Kafri
Full Thesis textFull thesis text - English Version


Abstract

Active systems are non-equilibrium systems in which the particles can convert ambient energy into a directional motion on the microscopic level. An example for a model of active particles is run-and-tumble particles where each particle moves at a constant velocity, but occasionally changes its direction of motion through a stochastic internal process. This model corresponds to the motion of an Escherichia Coli bacterium, which has been greatly studied in experimental environments. Active systems are not constrained by the second law of thermodynamics, and can be used to generate work on passive objects inside the system and drive them in a direction determined by their asymmetry as demonstrated in previous work. Other non-equilibrium phenomena, such as applying different pressures on different types of walls and mediating forces between passive bodies at rest, were also shown. It is a point of interest to develop a mathematical formalism to describe the interaction of an active system with a passive body submerged in it.

In this research we explore the equations of motions for a symmetric object submerged in a bath of Brownian or active particles derived from the Fokker-Planck equations of the microscopic particles, and provide a method to calculate the damping coefficient and force autocorrelation for both Brownian and active run-and-tumble systems, and develop a perturbative approach in the strength of the potentials which provides a method to obtain the damping coefficient and force autocorrelation to leading order in the potential strength for a general potential.

An exact calculation of the force autocorrelation for a piecewise constant potential in a medium of Brownian particles shows a powerlaw decay of t-0.5 for short times and t-1.5 for long times, where the transition occurs at a time exponentially large with the potential strength. A perturbative calculation in the case of a Gaussian potential is carried to sub-leading order in the potential and is confirmed numerically using Monte Carlo simulations. Calculation of the damping coefficient and force autocorrelation to leading order in the potential for a system of run-and-tumble particles shows that fluctuation-dissipation is violated for the passive object, which means that its motion cannot be simply described by an effective temperature.