Python代写 | Project for MSDM5003: Stochastic simulation for an active Brownian particle

本次日本代写是一个Python物理学的project

1. Background

Self-propelled Brownian particles have come under the spotlight of the physical and biophysical
research communities. These active particles are biological or man-made microscopic and nanoscopic
objects that can propel themselves by taking up energy from their environment and converting it into
directed motion. On the one hand, self-propulsion is a common feature in microorganisms and allows
for a more efficient exploration of the environment when looking for nutrients or running away from
toxic substances. On the other hand, tremendous progress has recently been made toward the fabrication
of artificial microswimmers and nanoswimmers that can self-propel based on different propulsion
mechanisms.

Figure 1. Self-propelled Brownian particles are biological or man-made objects capable of taking up
energy from their environment and converting it into directed motion. They are microscopic and
nanoscopic in size and have propulsion speeds (typically) up to a fraction of a millimeter per second.

2. Model: active Brownian motion
Consider a self-propelled particle with velocity v. The direction of motion is subject to rotational
diffusion, which leads to a coupling between rotation and translation. The corresponding stochastic
differential equations in 2-dimensional space are