This post describes the notation I’ll use elsewhere to discuss differential equation problems.
Selected Publications
A Sequential Nanopore-Channel Device for Polymer Separation
In this work, we investigated whether a series of nanopores connected by channels can be used to separate polymer mixtures by molecular size. We conducted multiscale coarse-grained simulations of semiflexible polymers driven through such a device. Polymers were modelled as chains of beads near the nanoporesand as single particles in the bulk of the channels. Since polymers rarely escape back into the bulk of the channels after coming sufficiently close to the nanopores, the more computationally expensive simulations near the pores were decoupled from those in the bulk. The distribution of polymer positions after many translocations was deduced mathematically from simulations across a single nanopore-channel pair, under the reasonable assumption of identical and independent dynamics in each channel and each nanopore. Our results reveal rich polymer dynamics in the the nanopore-channel device, and suggest that it can indeed produce polymer separation. As expected, the mean time to translocate across a single nanopore increases with chain length. Conversely, the mean time to cross the channels from one nanopore to the next decreases with chain length, as smaller chains explore more of the channel volume between translocations. As such, the time between translocations is a function of the length and width of the channels. Depending on the channel dimensions, polymers are sorted by increasing length, decreasing length, or non-monotonically by length such that polymers of an intermediate size emerge first. [J. Chem. Phys. 149, 174903 (2018); https://doi.org/10.1063/1.5037449]
A Sequential Nanopore-Channel Device for Polymer Separation,
2018
Neural Networks Trained to Solve Differential Equations Learn General Representations
We studied the internal structure of deep neural networks trained to solve a parametrized family of boundary value problems. Using the SVCCA, we showed that the first layers reliably discover generalized coordinates over the input domain. These representations are general over a range of problem parameters.
Currently available on arXiv,
2018
DNA Translocations through Nanopores under Nanoscale Preconfinement
We demonstrate nanoscale preconfinement of translocating molecules using an ultrathin nanoporous silicon nitride membrane separated from a single sensing nanopore by a nanoscale cavity. We present comprehensive experimental and simulation results demonstrating that this device eliminates the dependence of molecular passage time distributions on pore size. Furthermore, we show that this enables a more reliable DNA length separation independent of pore size and stability. We also demonstrate that the geometry can suppress the frequency of folded translocations, ensuring single-file passage of captured DNA molecules.
Nano Letters,
2018
Translocation Time through a Nanopore with an Internal Cavity Is Minimal for Polymers of Intermediate Length
We simulated the passage of polymers driven by an electric field through a nanocavity bounded by two nanopores. The translocation process is fastest for chains of intermediate length. Small chains become entropically trapped in the cavity. Long chains take longer to translocate because they experience more drag, and because they are simply longer.
Physical Review Letters,
2016