13 citations · 21 across the 7 of their papers we have counts for
7 papers
Small-time asymptotics and the emergence of complex singularities for the KdV equation
Scott W. McCue, Christopher J. Lustri, Daniel J. VandenHeuvel +3
While real-valued solutions of the Korteweg--de Vries (KdV) equation have been studied extensively over the past 50 years, much less attention has been devoted to solution behaviou…
A sparse -finite element method for piecewise-smooth differential equations with periodic boundary conditions
Daniel VandenHeuvel, Sheehan Olver
We develop an efficient -finite element method for piecewise-smooth differential equations with periodic boundary conditions, using orthogonal polynomials defined on circular a…
Pushing coarse-grained models beyond the continuum limit using equation learning
Daniel J. VandenHeuvel, Pascal R. Buenzli, Matthew J. Simpson
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processe…
Locating complex singularities of Burgers' equation using exponential asymptotics and transseries
Christopher J. Lustri, Ines Aniceto, Daniel J. VandenHeuvel +1
Burgers' equation is an important mathematical model used to study gas dynamics and traffic flow, among many other applications. Previous analysis of solutions to Burgers' equation…
Burgers' equation in the complex plane
Daniel J. VandenHeuvel, Christopher J. Lustri, John R. King +2
Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following o…
Mean exit time in irregularly-shaped annular and composite disc domains
Elliot J. Carr, Daniel J. VandenHeuvel, Joshua M. Wilson +1
Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass tra…
Mean exit time for diffusion on irregular domains
Matthew J Simpson, Daniel J Vandenheuvel, Joshua M Wilson +2
Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution o…