7 papers
Compatibility of Higher-Order Slow-Manifold Reduction and Continuum Limits in Adaptive Networks
Christian Kuehn, Fergal Murphy, Jan-Eric Sulzbach
Adaptive networks couple the evolution of node states to the evolution of the interactions between them. In fast-adapting phase oscillator networks, a slow-manifold reduction of a…
Thin Domains, Reduction, and Slow Manifolds
Christian Kuehn, Jan-Eric Sulzbach
We propose a unified framework for dimension reduction of partial differential equations posed on thin domains. Our approach combines three complementary ingredients: a careful bou…
On a Continuum Model for Random Genetic Drift: A Dynamic Boundary Condition Approach
Chun Liu, Jan-Eric Sulzbach, Yiwei Wang
We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equatio…
Non-isothermal diffuse interface model for phase transition and interface evolution
Chun Liu, Jan-Eric Sulzbach, Yiwei Wang
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is c…
Energetic Derivation and Geometric Reduction of Reaction-Diffusion Systems with Holling-Type Functional Responses
Jan-Eric Sulzbach
This paper presents an energetic derivation of a class of multi-species reaction-diffusion systems incorporating various functional responses, with a focus on and application to ec…
Approximate Slow Manifolds in the Fokker-Planck Equation
Christian Kuehn, Jan-Eric Sulzbach
In this paper we study the dynamics of a fast-slow Fokker-Planck partial differential equation (PDE) viewed as the evolution equation for the density of a multiscale planar stochas…