This article describes a local error estimator for Glimm＇s scheme for hyperbolic systems of conservation laws and uses it to replace the usual random choice in Glimm＇s scheme by an optimal choice. As a by-product of...This article describes a local error estimator for Glimm＇s scheme for hyperbolic systems of conservation laws and uses it to replace the usual random choice in Glimm＇s scheme by an optimal choice. As a by-product of the local error estimator, the procedure provides a global error estimator that is shown numerically to be a very accurate estimate of the error in L1 （R） for all times. Although there is partial mathematical evidence for the error estimator proposed, at this stage the error estimator must be considered ad- hoc. Nonetheless, the error estimator is simple to compute, relatively inexpensive, without adjustable parameters and at least as accurate as other existing error estimators. Numerical experiments in 1-D for Burgers＇ equation and for Euler＇s system are performed to measure the asymptotic accuracy of the resulting scheme and of the error estimator.展开更多
We report the electrical detection of captured gases through measurement of the quantum tunneling characteristics of gas-mediated molecular junctions formed across nanogaps.The gas-sensing nanogap device consists of a...We report the electrical detection of captured gases through measurement of the quantum tunneling characteristics of gas-mediated molecular junctions formed across nanogaps.The gas-sensing nanogap device consists of a pair of vertically stacked gold electrodes separated by an insulating 6 nm spacer(~1.5 nm of sputteredα-Si and~4.5 nm ALD SiO2),which is notched~10 nm into the stack between the gold electrodes.The exposed gold surface is functionalized with a self-assembled monolayer(SAM)of conjugated thiol linker molecules.When the device is exposed to a target gas(1,5-diaminopentane),the SAM layer electrostatically captures the target gas molecules,forming a molecular bridge across the nanogap.The gas capture lowers the barrier potential for electron tunneling across the notched edge region,from~5 eV to~0.9 eV and establishes additional conducting paths for charge transport between the gold electrodes,leading to a substantial decrease in junction resistance.We demonstrated an output resistance change of>108 times upon exposure to 80 ppm diamine target gas as well as ultralow standby power consumption of<15 pW,confirming electron tunneling through molecular bridges for ultralow-power gas sensing.展开更多
基金supported by a Korea Research Foundation Grant from the Korean Government(MOEHRD)(KRF-2007-331-C00053)supported by the National Science and Engineering Council of Canada and the Canadian Foundation for Innovation
文摘This article describes a local error estimator for Glimm＇s scheme for hyperbolic systems of conservation laws and uses it to replace the usual random choice in Glimm＇s scheme by an optimal choice. As a by-product of the local error estimator, the procedure provides a global error estimator that is shown numerically to be a very accurate estimate of the error in L1 （R） for all times. Although there is partial mathematical evidence for the error estimator proposed, at this stage the error estimator must be considered ad- hoc. Nonetheless, the error estimator is simple to compute, relatively inexpensive, without adjustable parameters and at least as accurate as other existing error estimators. Numerical experiments in 1-D for Burgers＇ equation and for Euler＇s system are performed to measure the asymptotic accuracy of the resulting scheme and of the error estimator.
基金We would like to acknowledge the contributions of Prattaydeepta Kairy,Chayanjit Ghosh,and Navid Farhoudi for assisting with various aspects of the sensor testing.This work made use of University of Utah USTAR shared facilities supported,in part,by the MRSEC Program of NSF under Award No.DMR-1121252This work was sponsored under cooperative agreement HR0011-15-2-0049 of the DARPA N-ZERO programThis research work was also generously funded by the cooperative agreement of DE-AR0001064 of the ARPAE OPEN 2018 program(Program Manager Dr.David Babson)in the United States.We feel grateful for the generous technical and administrative support from the ARPAE technical support staff(Dr.David Lee and Dr.Mike Xiao-Zhu Fan).
文摘We report the electrical detection of captured gases through measurement of the quantum tunneling characteristics of gas-mediated molecular junctions formed across nanogaps.The gas-sensing nanogap device consists of a pair of vertically stacked gold electrodes separated by an insulating 6 nm spacer(~1.5 nm of sputteredα-Si and~4.5 nm ALD SiO2),which is notched~10 nm into the stack between the gold electrodes.The exposed gold surface is functionalized with a self-assembled monolayer(SAM)of conjugated thiol linker molecules.When the device is exposed to a target gas(1,5-diaminopentane),the SAM layer electrostatically captures the target gas molecules,forming a molecular bridge across the nanogap.The gas capture lowers the barrier potential for electron tunneling across the notched edge region,from~5 eV to~0.9 eV and establishes additional conducting paths for charge transport between the gold electrodes,leading to a substantial decrease in junction resistance.We demonstrated an output resistance change of>108 times upon exposure to 80 ppm diamine target gas as well as ultralow standby power consumption of<15 pW,confirming electron tunneling through molecular bridges for ultralow-power gas sensing.
