4 papers
Modelling visibility and surface deformation in particle-fluid flow fields generated by helicopter rotors
Stephen Langdon, David J. Needham
As a helicopter descends towards a bed of sand, a high velocity particle laden cloud can form around the helicopter body, a phenomenon known as "brownout", and a consequence of whi…
The 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 3. The effect of perturbations in the kernel
David John Needham, John Billingham
In the third part of this series of papers, we address the same Cauchy problem that was considered in part 1, namely the nonlocal Fisher-KPP equation in one spatial dimension, $u_t…
A note on time-asymptotic bounds with a sharp algebraic rate and a transitional exponent for the sublinear Fujita problem
David John Needham, John Christopher Meyer
This note establishes sharp time-asymptotic algebraic rate bounds for the classical evolution problem of Fujita, but with sublinear rather than superlinear exponent. A transitional…
KPP fronts in shear flows with cut-off reaction rates
D. J. Needham, A. Tzella
We consider the effect of a shear flow which has, without loss of generality, a zero mean flow rate, on a Kolmogorov--Petrovskii--Piscounov (KPP) type model in the presence of a di…