Materials (e.g., brick or wood) are generally perceived as unintelligent. Even the highly researched “smart” materials only have extremely primitive analytical functions (e.g., simple logical operations). Here, a material is shown to have the ability to perform (i.e., without a computer) the advanced mathematical operation of calculus: the temporal derivative. It consists of a stimuli-responsive material coated asymmetrically with an adaptive impermeable layer. Its ability to analyze the derivative is shown by experiments, numerical modeling, and theory (i.e., scaling between derivative and response). This novel class of freestanding stimuli-responsive materials is demonstrated to serve effectively as a derivative controller for controlled delivery and self-regulation. Its fast response realizes the same designed function as complex industrial derivative controllers widely used in manufacturing — hence, materials can control processes with industrial-level functionality and efficiency. These results illustrate the possibility to associate specifically designed materials directly with higher concepts of mathematics for the development of “intelligent” material-based systems.
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This work was financially supported by the Ministry of Education, Singapore, under grant R-279-000-576-114 and R-279-000-535-114. FYL is grateful to Agency for Science, Technology and Research (A*STAR) for providing financial support under the PHAROS Advanced Surfaces Programme (grant number 1523700101, IHPC project id 13001345).