During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in...During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in a conference focusing on recent developments in"Optimization,Shape analysis,High-dimensional differential equations in science and Engineering,and machine learning Research(OSHER)"This conference hosted in-person talks by mathematicians,scientists,and industrial professionals worldwide.Those who could not attend extended their warm regards and expressed their appreciation for Professor Osher.展开更多
We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field t...We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field theory and derive,in a non-parametric setting,the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape.The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized.The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses(VIA).展开更多
We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation.The solver uses a level set framework to represent sharp,complex interfaces in a sim...We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation.The solver uses a level set framework to represent sharp,complex interfaces in a simple and robust manner.It also uses non-graded,adaptive octree grids which,in comparison to uniform grids,drastically decrease memory usage and runtime without sacrificing accuracy.The basic solver was introduced in earlier works[16,27],and here is extended to address biomolecular systems.First,a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained;this allows to accurately represent the location of the molecule’s surface.Next,a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface.Since the interface is implicitly represented by a level set function,imposing the jump boundary conditions is straightforward and efficient.展开更多
文摘During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in a conference focusing on recent developments in"Optimization,Shape analysis,High-dimensional differential equations in science and Engineering,and machine learning Research(OSHER)"This conference hosted in-person talks by mathematicians,scientists,and industrial professionals worldwide.Those who could not attend extended their warm regards and expressed their appreciation for Professor Osher.
文摘We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field theory and derive,in a non-parametric setting,the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape.The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized.The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses(VIA).
基金supported in part by the W.M.Keck Foundation,by the Institute for Collaborative Biotechnologies through contract no.W911NF-09-D-0001 from the U.S.Army Research Officeby ONR under grant agreement N00014-11-1-0027+1 种基金by the National Science Foundation under grant agreement CHE 1027817by the Department of Energy under grant agreement DE-FG02-08ER15991.
文摘We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation.The solver uses a level set framework to represent sharp,complex interfaces in a simple and robust manner.It also uses non-graded,adaptive octree grids which,in comparison to uniform grids,drastically decrease memory usage and runtime without sacrificing accuracy.The basic solver was introduced in earlier works[16,27],and here is extended to address biomolecular systems.First,a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained;this allows to accurately represent the location of the molecule’s surface.Next,a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface.Since the interface is implicitly represented by a level set function,imposing the jump boundary conditions is straightforward and efficient.
