Observation of super-ballistic Brownian dynamics in liquid
Data files
Jan 13, 2026 version files 53.35 MB
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barium_titanate_in_acetone_position.csv
13.75 MB
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barium_titanate_in_acetone_velocity.csv
12.81 MB
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conditioning.ipynb
20.55 KB
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fitting.ipynb
25.64 KB
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noise_position.csv
14 MB
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noise_velocity.csv
12.74 MB
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README.md
3.60 KB
Abstract
Brownian motion is a foundational physical process characterized by a mean-squared displacement that scales linearly in time in thermal equilibrium, known as diffusion. At short times, the mean squared displacement becomes ballistic, scaling as t2. This effect was predicted by Einstein in 1907 and recently observed experimentally. We report that this picture is only true on average; by conditioning specific initial velocities, we predict theoretically and confirm by experiment that the mean squared displacement becomes super-ballistic, with a power scaling law of t5/2. This result is due to the colored noise of incompressible fluids, resulting in a non-zero first moment for the thermal force when conditioned on non-zero initial velocities. These results are a first step towards unraveling the non-equilibrium dynamics of fluids.
Dataset DOI: 10.5061/dryad.pvmcvdnz4
Description of the data and file structure
We have constructed an optical trap for microspheres in a microfluidic chamber. We tracked the position of the trapped sphere below its momentum relaxation time and digitized the analog signal. We then conditioned on initial velocities to study short-time Brownian motion.
Files and variables
File: noise_velocity.csv
Description: Experimental velocity time traces but with no particle trapped. Demonstrates the system's noise due to the laser shot noise and other low frequency noise sources.
Variables
- Trace 1: Independent velocity time trace with 750 ns time step.
- Trace 2: Independent velocity time trace with 750 ns time step.
- Trace 3: Independent velocity time trace with 750 ns time step.
- Trace 4: Independent velocity time trace with 750 ns time step.
- Trace 5: Independent velocity time trace with 750 ns time step.
File: noise_position.csv
Description: Experimental position time traces but with no particle trapped. Demonstrates the system's noise due to the laser shot noise and other low frequency noise sources.
Variables
- Trace 1: Independent position time trace with 750 ns time step.
- Trace 2: Independent position time trace with 750 ns time step.
- Trace 3: Independent position time trace with 750 ns time step.
- Trace 4: Independent position time trace with 750 ns time step.
- Trace 5: Independent position time trace with 750 ns time step.
File: barium_titanate_in_acetone_velocity.csv
Description: Experimental velocity time trace for optically trapped microsphere.
Variables
- Trace 1: Independent velocity time trace with 750 ns time step.
- Trace 2: Independent velocity time trace with 750 ns time step.
- Trace 3: Independent velocity time trace with 750 ns time step.
- Trace 4: Independent velocity time trace with 750 ns time step.
- Trace 5: Independent velocity time trace with 750 ns time step.
File: barium_titanate_in_acetone_position.csv
Description: Experimental position time trace for optically trapped microsphere.
Variables
- Trace 1: Independent position time trace with 750 ns time step.
- Trace 2: Independent position time trace with 750 ns time step.
- Trace 3: Independent position time trace with 750 ns time step.
- Trace 4: Independent position time trace with 750 ns time step.
- Trace 5: Independent position time trace with 750 ns time step.
File: fitting.ipynb
Description: File contains the code that is used to fit the hydrodynamic theory to the equilibrium MSD data. We use a fixed barium titanate density and find the average radius, trap strength, and volts/meter conversion between the fits on the MSDs from the five independent time traces.
File: conditioning.ipynb
Description: File contains the code used to condition data and compare to theory. Functions directly corresponding to equations from the text are compared to conditioned MSDs.
Code/software
All of the scripts can be run inside a python environment with standard packages. The raw data is loaded into the fitting file that outputs processed time traces. These time traces are the data files provided. These can then be put into the conditioning file to extract conditioned MSDs.
Access information
Other publicly accessible locations of the data:
- none
Data was collected in the experimental Raizen lab at the University of Texas at Austin