Modeling Brownian Motion as a Timelapse of the Physical, Persistent Trajectory.

Area of Science:

• Physics
• Physical Chemistry
• Computational Science

Background:

• Diffusion is commonly modeled as a random walk, assuming memoryless trajectories and step lengths.
• These assumptions can lead to significant inaccuracies in describing particle movement.
• Understanding the physical trajectory of Brownian motion is crucial for accurate simulations.

Purpose of the Study:

• To analyze the accuracy of the random walk model for physical Brownian particle trajectories.
• To investigate the conditions under which subsampled trajectories exhibit memorylessness.
• To quantify the differences between subsampled and diffusional step length distributions.

Main Methods:

• Analysis of 'timelapses' of physical trajectories.
• Calculation over collisional time scales using a velocity autocorrelation function.
• Incorporation of hydrodynamic and acoustic solvent effects.

Main Results:

• Subsampled trajectories achieve genuine memorylessness only when the time step exceeds relaxation time by ~200x.
• Subsampled step length distributions show variances significantly smaller (by ~2x) than diffusional ones.
• Diffusional displacements are superballistic at short time scales; subsampled trajectories act as moving averages.

Conclusions:

• The standard random walk model oversimplifies Brownian motion, leading to errors.
• Physical trajectory mean squared displacement (MSD) approaches 2Dt, but subsampled MSD does not.
• Computational methods need adjustments to account for these discrepancies in modeling diffusion.