Dr Andrew Krause | Mathematical Institute

Dr Andrew Krause

B.S., M.S., DPhil

Postdoctoral Research Assistant

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Personal Website:

https://www.andrewkrause.org/

CV (301.93K)

+44 1865 615166

Address

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

Recent Publications:

Hybrid approach to modeling spatial dynamics of systems with generalist predators

Hybrid approach to modeling spatial dynamics of systems with generalist predators
Fussell, EF; Krause, AL; Van Gorder, RA;
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, AL;
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, AL; Ellis, MA; Van Gorder, RA;
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, AL; Castillo, JA; Padilla, P;
Journal of theoretical biology (25 September 2018)

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

Effects of tidal torques on 1I/2017 U1 ('Oumuamua)
Kwiecinski, JA; Krause, AL; Van Gorder, RA;
ICARUS volume 311 page 170-174 (1 September 2018) Full text available

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
Van Gorder, RA; Krause, AL; Brosa Planella, F; Burton, AM;
Annals of Physics volume 396 page 397-428 (1 September 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, RM; Krause, AL; Fadai, NT; Van Gorder, RA;
Journal of Theoretical Biology volume 451 page 19-34 (14 August 2018)

Lattice and continuum modelling of a bioactive porous tissue scaffold.

Lattice and continuum modelling of a bioactive porous tissue scaffold.
Krause, AL; Beliaev, D; Van Gorder, RA; Waters, SL;
Mathematical medicine and biology : a journal of the IMA (10 August 2018)

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

Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies
Krause, AL; Kurowski, L; Yawar, K; Van Gorder, RA;
Journal of Theoretical Biology volume 449 page 35-52 (14 July 2018)

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems.

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems.
Krause, AL; Klika, V; Woolley, TE; Gaffney, EA;
Physical review. E issue 5-1 volume 97 page 052206- (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
Kwiecinski, JA; Kovacs, A; Krause, AL; Planella, FB; Van Gorder, RA;
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS issue 5 volume 28 (May 2018) Full text available

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

Emergent structures in reaction-advection-diffusion systems on a sphere
Krause, AL; Burton, AM; Fadai, NT; Van Gorder, RA;
Physical Review E issue 4 volume 97 (23 April 2018)

Two-Species Migration and Clustering in Two-Dimensional Domains.

Two-Species Migration and Clustering in Two-Dimensional Domains.
Kurowski, L; Krause, AL; Mizuguchi, H; Grindrod, P; Van Gorder, RA;
Bulletin of mathematical biology issue 10 volume 79 page 2302-2333 (October 2017)

Continuous dispersal in a model of predator-prey-subsidy population dynamics

Continuous dispersal in a model of predator-prey-subsidy population dynamics
Bassett, A; Krause, AL; Van Gorder, RA;
ECOLOGICAL MODELLING volume 354 page 115-122 (24 June 2017) Full text available

Dynamics of the non-autonomous stochastic p-Laplace equation driven by multiplicative noise

Dynamics of the non-autonomous stochastic p-Laplace equation driven by multiplicative noise
Krause, A; Lewis, M; Wang, B;
APPLIED MATHEMATICS AND COMPUTATION volume 246 page 365-376 (1 November 2014) Full text available

Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains

Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains
Krause, A; Wang, B;
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS issue 2 volume 417 page 1018-1038 (15 September 2014) Full text available

Generic amplitude death in coupled complex Ginzburg-Landau systems

Generic amplitude death in coupled complex Ginzburg-Landau systems
Gorder, RAV; Krause, AL; Kwiecinski, JA;
Full text available

Bifurcations and Dynamics Emergent From Lattice and Continuum Models of Bioactive Porous Media

Bifurcations and Dynamics Emergent From Lattice and Continuum Models of Bioactive Porous Media
Krause, AL; Beliaev, D; Van Gorder, RA; Waters, SL;
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS issue 11 volume 28 (October 2018) Full text available

Asymptotic Dynamics of Stochastic $p$-Laplace Equations on Unbounded Domains

Asymptotic Dynamics of Stochastic $p$-Laplace Equations on Unbounded Domains
Krause, A;
Full text available

krause@maths.ox.ac.uk

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.

A summary of some work from 2017 can be found here.

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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