853 research outputs found
Physical limits to sensing material properties
Constitutive relations describe how materials respond to external stimuli
such as forces. All materials respond heterogeneously at small scales, which
limits what a localized sensor can discern about the global constitution of a
material. In this paper, we quantify the limits of such constitutional sensing
by determining the optimal measurement protocols for sensors embedded in
disordered media. For an elastic medium, we find that the least fractional
uncertainty with which a sensor can determine a material constant
is approximately
\begin{equation*}
\frac{\delta \lambda_0}{\lambda_0 } \sim \left( \frac{\Delta_{\lambda} }{
\lambda_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{
\xi }{ a } \right)^{D/2} \end{equation*} for , , and , where is the size of the sensor, is
its spatial resolution, is the correlation length of fluctuations in the
material constant, is the local variability of the material
constant, and is the dimension of the medium. Our results reveal how one
can construct microscopic devices capable of sensing near these physical
limits, e.g. for medical diagnostics. We show how our theoretical framework can
be applied to an experimental system by estimating a bound on the precision of
cellular mechanosensing in a biopolymer network.Comment: 33 pages, 3 figure
Elastic heterogeneity of soft random solids
Spatial heterogeneity in the elastic properties of soft random solids is
investigated via a two-pronged approach. First, a nonlocal phenomenological
model for the elastic free energy is examined. This features a quenched random
kernel, which induces randomness in the residual stress and Lame coefficients.
Second, a semi-microscopic model network is explored using replica statistical
mechanics. The Goldstone fluctuations of the semi-microscopic model are shown
to reproduce the phenomenological model, and via this correspondence the
statistical properties of the residual stress and Lame coefficients are
inferred. Correlations involving the residual stress are found to be
long-ranged and governed by a universal parameter that also gives the mean
shear modulus.Comment: 5 page
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