传感材料特性的物理限制
Physical limits to sensing material properties
摘要：
本构关系描述了材料如何响应外部刺激，如力。所有材料在小尺度上的反应都是不均匀的，这限制了局部传感器对材料整体结构的识别。在本文中，我们量化的限制，这样的宪法感测，通过确定最佳的测量协议嵌入在无序介质中的传感器。对于弹性介质，我们发现，传感器可以确定材料常数$λ_0$的最小分数不确定度对于$a \gg d \gg ξ$、$λ_0 \gg Δ_λ^{1/2}$和$D>1$近似为\begin{equation*} \frac{δλ_0}{λ_0 } \sim \left( \frac{Δ_λ }{ λ_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{ ξ}{ a } \right)^{D/2} \end{equation*}，其中$a$是传感器的尺寸，$d$是其空间分辨率，$ξ$是材料常数波动的相关长度，$Δ_λ$是材料常数的局部变化，并且$D$是介质的维度。我们的研究结果揭示了如何构建能够在这些物理极限附近进行传感的微观设备，例如用于医疗诊断。我们展示了我们的理论框架如何可以应用到一个实验系统，通过估计一个生物聚合物网络中的细胞mechanosensing的精度上的界限。
英文摘要：
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 $λ_0$ is approximately \begin{equation*} \frac{δλ_0}{λ_0 } \sim \left( \frac{Δ_λ }{ λ_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{ ξ}{ a } \right)^{D/2} \end{equation*} for $a \gg d \gg ξ$, $λ_0 \gg Δ_λ^{1/2}$, and $D>1$, where $a$ is the size of the sensor, $d$ is its spatial resolution, $ξ$ is the correlation length of fluctuations in the material constant, $Δ_λ$ is the local variability of the material constant, and $D$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
