Dr Andrew Krause | Mathematical Institute

Dr Andrew Krause

B.S., M.S., DPhil

Status:

Postdoctoral Research Assistant

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Personal website:

https://www.andrewkrause.org/

CV (348.39K)

+44 1865 615166

ORCID iD:

https://orcid.org/0000-0001-9638-7278

Research groups:

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Recent Publications:

Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices

Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices
Van Gorder, R; Krause, A; Malomed, B; Kaup, D
Communications in Nonlinear Science and Numerical Simulation volume 85 (1 June 2020)

Predicting bone formation in MSC seeded hydrogels using experiment based mathematical modelling

Predicting bone formation in MSC seeded hydrogels using experiment based mathematical modelling
El Haj, A; Waters, S; Krause, A; Price, J
Tissue Engineering Part A (17 March 2020)

Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion.

Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion.
Strobl, M; Krause, A; Damaghi, M; Gillies, R; Anderson, A; Maini, P
Bulletin of mathematical biology issue 1 volume 82 page 15- (17 January 2020)

Generalist predator dynamics under kolmogorov versus non-Kolmogorov models.

Generalist predator dynamics under kolmogorov versus non-Kolmogorov models.
Xu, Y; Krause, A; Van Gorder, R
Journal of theoretical biology volume 486 page 110060-110060 (2 November 2019)

Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains

Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains
Krause, A; Kim, H; Van Gorder, R
Journal of Fluid Mechanics volume 877 page 759-823 (27 August 2019)

Amplitude death criteria for coupled complex Ginzburg–Landau systems

Amplitude death criteria for coupled complex Ginzburg–Landau systems
Van Gorder, R; Krause, A; Kwiecinski, J
Nonlinear Dynamics (4 May 2019)

Hybrid approach to modeling spatial dynamics of systems with generalist predators

Hybrid approach to modeling spatial dynamics of systems with generalist predators
Fussell, E; Krause, A; Van Gorder, R
Journal of Theoretical Biology volume 462 page 26-47 (7 February 2019)

Beyond Onsager–Casimir Relations: Shared Dependence of Phenomenological Coefficients on State Variables

Beyond Onsager–Casimir Relations: Shared Dependence of Phenomenological Coefficients on State Variables
Klika, V; Krause, A
The Journal of Physical Chemistry Letters page 7021-7025 (5 December 2018)

Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds

Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds
Krause, A; Ellis, M; Van Gorder, R
Bulletin of Mathematical Biology (3 December 2018)

Turing–Hopf patterns on growing domains: The torus and the sphere

Turing–Hopf patterns on growing domains: The torus and the sphere
Sánchez-Garduño, F; Krause, A; Castillo, J; Padilla, P
Journal of Theoretical Biology volume 481 page 136-150 (25 September 2018)

Lattice and continuum modelling of a bioactive porous tissue scaffold

Lattice and continuum modelling of a bioactive porous tissue scaffold
Krause, A; Beliaev, D; Gorder, R; Waters, S
arXiv issue 3 volume 36 page 325-360 (September 2019)

Coupled complex Ginzburg–Landau systems with saturable nonlinearity and asymmetric cross-phase modulation

Coupled complex Ginzburg–Landau systems with saturable nonlinearity and asymmetric cross-phase modulation
Gorder, R; Krause, A; Burton, A; Planella, F
Annals of Physics volume 396 page 397-428 (19 July 2018)

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems
Krause, A; Klika, V; Gaffney, E; Woolley, T
Physical Review E issue 5 volume 97 page 052206- (14 May 2018)

Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations

Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations
Krause, A; Planella, F; Van Gorder, R; Kwiecinski, J; Kovacs, A
International Journal of Bifurcation and Chaos issue 5 volume 25 (1 May 2018)

Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays

Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays
Eide, R; Kruase, A; Fadai, N; Van Gorder, R
Journal of Theoretical Biology volume 451 page 19-34 (1 May 2018)

Emergent structures in reaction-advection-diffusion systems on a sphere

Emergent structures in reaction-advection-diffusion systems on a sphere
Fadai, N; Van Gorder, R; Krause, A; Burton, A
Physical Review E issue 4-1 volume 97 page 042215- (23 April 2018)

Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies

Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies
Krause, A; Van Gorder, R; Kurowski, L; Yawar, K
Journal of Theoretical Biology volume 449 page 35-52 (16 April 2018)

Effects of tidal torques on 1I/2017 U1 (‘Oumuamua)

Effects of tidal torques on 1I/2017 U1 (‘Oumuamua)
Kwiecinski, J; Krause, A; Van Gorder, R
Icarus volume 311 page 170-174 (4 April 2018)

Two-species migration and clustering in two-dimensional domains

Two-species migration and clustering in two-dimensional domains
Kurowski, L; Krause, A; Mizuguchi, H; Grindrod, P; Van Gorder, R
Bulletin of Mathematical Biology issue 10 volume 79 page 2302–2333- (1 August 2017)

Research interests:

Google Scholar Profile

I am broadly interested in nonlinear dynamical systems, with applications to mathematical biology and other areas. I am particularly interested in understanding and overcoming the limits of current methodologies to capture spatial and temporal complexity in situations of scientific interest. I am currently active in the following research areas:

Reaction-Diffusion Systems: pattern formation, diffusion-driven (Turing) instabilities, spatiotemporal phenomena (including chaos and heterogeneity), RD systems on static and growing manifolds, with applications to developmental biology, population dynamics, and tissue engineering.
Spatial Population Dynamics: discrete patch and spatially continuous models, random and deterministic dispersal, synchronization of metapopulations, and applications to ecological and epidemiological metapopulation models.
Nonlinear Dynamical Systems: dissipative dynamics (attractors and absorbing sets), numerical bifurcation analysis, and stochastic differential equations.

In all of these cases I am interested both in the scientific field or application, as well as in the theoretical or computational tools used. I primarily approach problems from a dynamical systems point of view, and I am keen to see applications motivate new theory in this field. However, I am much more motivated by developing approaches to solve problems as they are, rather than trying to force them into a particular shape in order to use a specific hammer. While I have used several tools in the past, I am more than happy to pick up new methodologies in order to address an interesting problem. I am also happy to pursue questions outside of my main research interests, as long as I am able to provide a useful perspective in addressing them.

Teaching:

TA: MT 2014-C5.7 Topics in Fluid Mechanics, HT 2015-MMSC B5.2 Applied Partial Differential Equations, MT 2015-MMSC Supplementary Applied Mathematics, HT 2016-MMSC Further Mathematical Methods

Departmental Tutor: MT 2016-C5.12 Mathematical Physiology

Pembroke Stipendiary Lectureship: MT 2017-Prelims Introductory Calculus, Part A Differential Equations I, HT 2018-Prelims Dynamics, Part A Differential Equations II, Waves and Fluids, Statistics, TT Part A Mathematical Biology, MT 2018-Prelims Calculus, Part A DEI, Quantum Theory

St. Anne's Stipendiary Lectureship: MT 2015-Prelims Introductory Calculus, Geometry, HT 2016-Part A Differential Equations 2, Integral Transforms

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