subcapillaries should combine to form a capillary with radius about larger, and dates to the early 19th century. Bryn Mawr physiologist Cecil D. Murray published the law's modern, general formulation in 1926, but it languished in a disciplinary no-man's-land for the next fifty years: too trivial for physicists and too complicated for biologists. Interest in the law revived in the 1970s. Applications In circulatory system governed by Murray's law with , shear stress on vessel walls is roughly constant. Consequently, variations in shear stress are a sign of deviation from Murray's law; Rodbard and Zamir suggest that such variations stimulate homeostatic growth or contraction. Murray's law rarely applies to engineered materials, because man-made transport routes attempt to reduce flow resistance by minimizing branching and maximizing diameter. Murray materials Materials that obey Murray's law at the microscale, known as Murray materials, are expected to have favorable flow characteristics, but their construction is difficult, because it requires tight control over pore size typically over a wide range of scales. Lim et al propose designing microfluidic "labs on a chip" in accord with Murray's law to minimize flow resistance during analysis. Conventional lithography does not support such construction, because it cannot produce channels of varying depth. Seeking long-lived lithium battery electrodes, Zheng et al constructed Murray materials out of layers of sintered zinc oxide nanoparticles. The evaporation rate of the dissolved zinc oxide solvent controlled the size of the pores in each layer; the network was then just layers of ZnO with different pore sizes placed atop each other. Because power plant working fluids typically funnel into many small tubules for efficient heat transfer, Murray's law may be appropriate for nuclear reactor design. References Footnotes Further reading Botany Equations Developmental biology