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Buffon's Brownian needles: harnessing thermal motion for stochastic sampling.

Charlie Maslen¹, Luke Nicholson¹, Juliane Simmchen^1,2

¹University of Strathclyde, 295 Cathedral Street, Glasgow G1 1XL, UK. juliane.simmchen@strath.ac.uk.

|November 6, 2025

Summary

This study physically implements Monte Carlo sampling using microscopic rods undergoing Brownian motion for Buffon's needle experiment. This soft matter approach offers a low-energy pathway for stochastic computation using thermal noise.

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Thermal Measurement Techniques in Analytical Microfluidic Devices

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Area of Science:

Physics
Soft Matter Physics
Computational Physics

Background:

Monte Carlo (MC) sampling is a computational technique.
Geometric probability problems are often complex to solve analytically.
Brownian motion is the random movement of particles suspended in a fluid.

Purpose of the Study:

To demonstrate a physical implementation of Monte Carlo sampling.
To apply this physical sampling to the classical Buffon's needle experiment.
To explore the use of soft matter systems for stochastic computation.

Main Methods:

Utilizing the Brownian motion of microscopic rods as a physical system.
Mapping a geometric probability problem (Buffon's needle) onto a Monte Carlo method.
Embedding experimental parameters (rod length) into the physical system to represent probability integrals.

Main Results:

Successfully demonstrated a physical realization of Monte Carlo sampling.
Showcased how thermal motion of rods can perform the sampling aspect of the computation.
Validated the approach using the Buffon's needle experiment as a toy model.

Conclusions:

Embedding probabilistic structure into soft matter enables stochastic computation.
This method provides a low-energy pathway for computation by exploiting thermal noise.
Physical implementations of computational methods can offer alternative approaches to traditional algorithms.