24 citations · 72 across the 28 of their papers we have counts for
30 papers
Microscopic Variability Alters Macroscopic Rotation Speed in Stochastic Spiral Waves
Jolien Kamphuis, Desmond Kabus, Hermen Jan Hupkes +1
We present a general theory for noise-induced corrections to the angular velocity of spiral waves. Stochasticity produces two second-order effects: an instantaneous term from heter…
Radiating Solitary Waves in an FPUT Lattice with Random Coefficients
Hermen Jan Hupkes, Joshua A. McGinnis, Rik W. S. Westdorp +1
We study the propagation of solitary waves in a Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with small random heterogeneity in the linear spring force. Perturbed by the random environm…
Stability of Stochastically Forced Solitons in the Korteweg-de Vries Equation
Rik W. S. Westdorp, Hermen Jan Hupkes
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statist…
Local Phase Tracking and Metastability of Planar Waves in Stochastic Reaction-Diffusion Systems
Mark van den Bosch, Hermen Jan Hupkes
Planar travelling waves on with are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescale…
Conditional Speed and Shape Corrections for Travelling Wave Solutions to Stochastically Perturbed Reaction-Diffusion Systems
Mark van den Bosch, Christian H. S. Hamster, Hermen Jan Hupkes
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equatio…
Small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou lattices
Timothy E. Faver, Hermen Jan Hupkes, J. Douglas Wright
We prove the existence of small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are inf…
Existence of monostable fronts for a KPP infinite-difference numerical scheme
Louis Garénaux, Hermen Jan Hupkes
We study the existence of traveling wave solutions for a numerical counterpart of the KPP equation. We obtain the existence of monostable fronts for all super-critical speeds in th…
Multidimensional Stability of Planar Travelling Waves for Stochastically Perturbed Reaction-Diffusion Systems
Mark van den Bosch, Hermen Jan Hupkes
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invarian…
Soliton Amplification in the Korteweg-de Vries Equation by Multiplicative Forcing
Rik W. S. Westdorp, Hermen Jan Hupkes
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation with small multiplicative forcing. Forcing breaks the conservative structure of the KdV equa…
Propagation reversal on trees in the large diffusion regime
Hermen Jan Hupkes, Mia Jukic
In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite -ary trees in the continuum regime where the diffusion parameter is large…
Mass and spring dimer Fermi-Pasta-Ulam-Tsingou nanopterons with exponentially small, nonvanishing ripples
Timothy E. Faver, Hermen Jan Hupkes
We study traveling waves in mass and spring dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices in the long wave limit. Such lattices are known to possess nanopteron traveling waves in…
Propagation reversal for bistable differential equations on trees
Hermen Jan Hupkes, Mia Jukić, Petr Stehlík +1
We study traveling wave solutions to bistable differential equations on infinite -ary trees. These graphs generalize the notion of classical square infinite lattices and our res…
Scaling Relations for Auxin Waves
Timothy E. Faver, Hermen Jan Hupkes, Roeland M. H. Merks +1
We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show…
SparseAlign: A Super-Resolution Algorithm for Automatic Marker Localization and Deformation Estimation in Cryo-Electron Tomography
Poulami Somanya Ganguly, Felix Lucka, Holger Kohr +3
Tilt-series alignment is crucial to obtaining high-resolution reconstructions in cryo-electron tomography. Beam-induced local deformation of the sample is hard to estimate from the…
Curvature-driven front propagation through planar lattices in oblique directions
Mia Jukić, Hermen Jan Hupkes
In this paper we investigate the long-term behaviour of solutions to the discrete Allen-Cahn equation posed on a two-dimensional lattice. We show that front-like initial conditions…
Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions
Willem M. Schouten-Straatman, Hermen Jan Hupkes
We investigate the impact of spatial-temporal discretisation schemes on the dynamics of a class of reaction-diffusion equations that includes the FitzHugh-Nagumo system. For the te…
Micropterons, Nanopterons and Solitary Wave Solutions to the Diatomic Fermi-Pasta-Ulam-Tsingou Problem
Timothy E. Faver, Hermen Jan Hupkes
We use a specialized boundary-value problem solver for mixed-type functional differential equations to numerically examine the landscape of traveling wave solutions to the diatomic…
Stability of Travelling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations
Christian Hamster, Hermen Jan Hupkes
In this paper we establish the meta-stability of travelling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the…
Atomic Super-Resolution Tomography
Poulami Somanya Ganguly, Felix Lucka, Hermen Jan Hupkes +1
We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called di…
Exponential Dichotomies for Nonlocal Differential Operators with Infinite Range Interactions
Willem M. Schouten-Straatman, Hermen Jan Hupkes
We show that MFDEs with infinite range discrete and/or continuous interactions admit exponential dichotomies, building on the Fredholm theory developed by Faye and Scheel for such…
Dynamics of curved travelling fronts for the discrete Allen-Cahn equation on a two-dimensional lattice
Mia Jukić, Hermen Jan Hupkes
In this paper we consider the discrete Allen-Cahn equation posed on a two-dimensional rectangular lattice. We analyze the large-time behaviour of solutions that start as bounded pe…
Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
Timothy E. Faver, Hermen Jan Hupkes
The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of alternating particles connected by identical nonlinear springs. We prove the existence of micropteron t…
Travelling Waves for Reaction-Diffusion Equations Forced by Translation Invariant Noise
Christian Hamster, Hermen Jan Hupkes
Inspired by applications, we consider reaction-diffusion equations on that are stochastically forced by a small multiplicative noise term that is white in time, colour…
Counting and ordering periodic stationary solutions of lattice Nagumo equations
Hermen Jan Hupkes, Leonardo Morelli, Petr Stehlík +1
We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs…