Selected Publications

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);]
A Sequential Nanopore-Channel Device for Polymer Separation, 2018

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

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

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

Recent Publications

. A Sequential Nanopore-Channel Device for Polymer Separation. A Sequential Nanopore-Channel Device for Polymer Separation, 2018.

PDF Source Document

. Neural Networks Trained to Solve Differential Equations Learn General Representations. Currently available on arXiv, 2018.


. DNA Translocations through Nanopores under Nanoscale Preconfinement. Nano Letters, 2018.


. Translocation Time through a Nanopore with an Internal Cavity Is Minimal for Polymers of Intermediate Length. Physical Review Letters, 2016.


Recent & Upcoming Talks

Neural Networks Trained to Solve Differential Equations Learn General Representations
Dec 4, 2018 10:45 AM

Recent Posts

This post describes the notation I’ll use elsewhere to discuss differential equation problems.


This post contains a brief overview on solving PDE problems directly using neural networks, including an overview of relevant literature.




Since 2017, I have been working at the UOIT Science Café. This is a weekly drop-in session open to all UOIT science students. I provide help with mathematics, physics, and computer science courses.

I also work as a teaching assistant. This entails reviewing lecture material in tutorials, providing focused help in office hours, and assisting with the administration and marking of assessments. I have been a teaching assistant for the following courses at UOIT:

  • Advanced Linear Algebra and Applications (MATH 2055)
  • Discrete Mathematics (MATH 2080/CSCI 2110)
  • Classical Mechanics (PHY 2030)
  • Linear Algebra for Engineers (MATH 1850)
  • Calculus 1 & 2 (MATH 1010 & 1020)
  • Physics 1 (PHY 1010)

I’ve also had the opportunity to present lectures on the following topics:

  • Quadratic forms for Advanced Linear Algebra and Applications (MATH 2055)
  • Bessel functions for Mathematical Physics (PHY 3040)