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Physical limits to sensing material properties

Author

Listed:
  • Farzan Beroz

    (University of Michigan)

  • Di Zhou

    (University of Michigan)

  • Xiaoming Mao

    (University of Michigan)

  • David K. Lubensky

    (University of Michigan)

Abstract

All materials respond heterogeneously at small scales, which limits what a sensor can learn. Although previous studies have characterized measurement noise arising from thermal fluctuations, the limits imposed by structural heterogeneity have remained unclear. In this paper, we find that the least fractional uncertainty with which a sensor can determine a material constant λ0 of an elastic medium is approximately $$\delta {\lambda }_{0}/{\lambda }_{0} \sim ({\Delta }_{\lambda }^{1/2}/{\lambda }_{0}){(d/a)}^{D/2}{(\xi /a)}^{D/2}$$ δ λ 0 / λ 0 ~ ( Δ λ 1 / 2 / λ 0 ) ( d / a ) D / 2 ( ξ / a ) D / 2 for a ≫ d ≫ ξ, $${\lambda }_{0}\gg {\Delta }_{\lambda }^{1/2}$$ λ 0 ≫ Δ λ 1 / 2 , and D > 1, where a is the size of the sensor, d is its spatial resolution, ξ is the correlation length of fluctuations in λ0, Δλ is the local variability of λ0, and D is the dimension of the medium. Our results reveal how one can construct devices capable of sensing near these limits, e.g. for medical diagnostics. We use our theoretical framework to estimate the limits of mechanosensing in a biopolymer network, a sensory process involved in cellular behavior, medical diagnostics, and material fabrication.

Suggested Citation

  • Farzan Beroz & Di Zhou & Xiaoming Mao & David K. Lubensky, 2020. "Physical limits to sensing material properties," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
  • Handle: RePEc:nat:natcom:v:11:y:2020:i:1:d:10.1038_s41467-020-18995-4
    DOI: 10.1038/s41467-020-18995-4
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