87 citations · 396 across the 37 of their papers we have counts for
9 papers · 1 filter
Pattern formation in a diffusion-ODE model with hysteresis
Anna Marciniak-Czochra, Madoka Nakayama, Izumi Takagi
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion…
Analysis of particle methods for structured population models with nonlocal boundary term in the framework of bounded Lipschitz distance
P. Gwiazda, J. Jabłoński, A. Marciniak-Czochra +1
Recently developed theoretical framework for analysis of structured population dynamics in the spaces of nonnegative Radon measures with a suitable metric provides a rigorous tool…
Clonal selection and therapy resistance in acute leukemias: Mathematical modelling explains different proliferation patterns at diagnosis and relapse
Thomas Stiehl, Natalia Baran, Anthony D. Ho +1
Recent experimental evidence suggests that acute myeloid leukemias may originate from multiple clones of malignant cells. Nevertheless it is not known how the observed clones may d…
Dynamical spike solutions in a nonlocal model of pattern formation
Anna Marciniak-Czochra, Steffen Härting, Grzegorz Karch +1
Coupling a reaction-diffusion equation with ordinary differential equations (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffus…
Efficient algorithms computing distances between Radon measures on R
Jedrzej Jablonski, Anna Marciniak-Czochra
In this paper numerical methods of computing distances between two Radon measures on R are discussed. Efficient algorithms for Wasserstein-type metrics are provided. In particular,…
Spike patterns in a reaction-diffusion-ode model with Turing instability
Steffen Härting, Anna Marciniak-Czochra
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such sy…
A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium
Anna Marciniak-Czochra, Andro Mikelic
We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous med…
Pressure jump interface law for the Stokes-Darcy coupling: Confirmation by direct numerical simulations
Thomas Carraro, Christian Goll, Anna Marciniak-Czochra +1
It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, interface law for the effective str…
Instability of Turing patterns in reaction-diffusion-ODE systems
Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such s…