Publications (47)
Center manifolds for stochastic evolution equations
Xiaopeng Chen, A. J. Roberts, Jinqiao Duan
Resolve the multitude of microscale interactions to model stochastic partial differential equations
A. J. Roberts
Computer algebra compares the stochastic superslow manifold of an averaged SPDE with that of the original slow-fast SPDE
A. J. Roberts
The prisoners may be in two minds
A. J. Roberts
The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems
A. J. Roberts
On the low-dimensional modelling of Stratonovich stochastic differential equations
Chao Xu, A. J. Roberts
Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations
J. E. Bunder, A. J. Roberts
Average and deviation for slow-fast stochastic partial differential equations
W. Wang, A. J. Roberts
Multiscale modelling couples patches of nonlinear wave-like simulations
Meng Cao, A. J. Roberts
The inertial dynamics of thin film flow of non-Newtonian fluids
A. J. Roberts
Better buffers for patches in macroscale simulation of systems with microscale randomness
J. E. Bunder, A. J. Roberts, I. G. Kevrekidis
A normal form of thin fluid film equations provides initial conditions
A. J. Roberts
Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible
A. J. Roberts
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
Yan Lv, A. J. Roberts
A flexible error estimate for the application of centre manifold theory
Zhenquan Li, A. J. Roberts
Multiscale modelling couples patches of two-layer thin fluid flow
Meng Cao, A. J. Roberts
Model dynamics on a multigrid across multiple length and time scales
A. J. Roberts
Normal form transforms separate slow and fast modes in stochastic dynamical systems
A. J. Roberts
Modelling the dynamics of turbulent floods
Z. Mei, A. J. Roberts, Zhenquan Li
Self similarity and attraction in stochastic nonlinear reaction-diffusion systems
Wei Wang, A. J. Roberts
Computer algebra derives correct initial conditions for low-dimensional dynamical models
A. J. Roberts
Model turbulent floods with the Smagorinski large eddy closure
A. J. Roberts, D. J. Georgiev, D. V. Strunin
Use the information dimension, not the Hausdorff
A. J. Roberts
Proper initial conditions for the lubrication model of the flow of a thin film of fluid
S. A. Suslov, A. J. Roberts
Long-wave models of thin film fluid dynamics
A. J. Roberts
Unbiased estimation of multi-fractal dimensions of finite data sets
A. J. Roberts, A. Cronin
Advection-dispersion in symmetric field-flow fractionation channels
S. A. Suslov, A. J. Roberts
Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domains
A. J. Roberts
Modelling suspended sediment in environmental turbulent fluids
Meng Cao, A. J. Roberts
Initialization and the quasi-geostrophic slow manifold
S. M. Cox, A. J. Roberts
On the approximation for singularly perturbed stochastic wave equations
Wei Wang, Yan Lv, A. J. Roberts
Large deviations for slow-fast stochastic partial differential equations
Wei Wang, A. J. Roberts, Jinqiao Duan
Slow manifold and averaging for slow-fast stochastic differential system
W. Wang, A. J. Roberts
Macroscale boundary conditions for a non-linear heat exchanger
Chen Chen, A. J. Roberts, J. E. Bunder
Holistic finite differences ensure fidelity to Burger's equation
A. J. Roberts
Low-dimensional modelling of a generalized Burgers equation
Zhenquan Li, A. J. Roberts
The accurate and comprehensive model of thin fluid flows with inertia on curved substrates
A. J. Roberts, Zhenquan Li
The Accurate Modelling of Thin 3D Fluid Flows with Inertia on Curved Substrates
Zhenquan Li, A. J. Roberts
A Lubrication Model of Coating Flows over a Curved Substrate in Space
R. Valery Roy, A. J. Roberts, M. E. Simpson
The Construction of Zonal Models of Dispersion in Channels via Matched Centre Manifolds
S. D. Watt, A. J. Roberts
Similarity, attraction and initial conditions in an example of nonlinear diffusion
S. A. Suslov, A. J. Roberts
Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain
Wei Wang, A. J. Roberts
Ion mediated crosslink driven mucous swelling kinetics
S. Sircar, A. J. Roberts
Macroscopic reduction for stochastic reaction-diffusion equations
Wei Wang, A. J. Roberts
Initial Conditions for Models of Dynamical Systems
Stephen M. Cox, A. J. Roberts
Low-Dimensional Modelling of Dynamics via Computer Algebra
A. J. Roberts
Choose interelement coupling to preserve self-adjoint dynamics in multiscale modelling and computation
A. J. Roberts