@article{BetaGovYochelis2020,
  author    = {Beta, Carsten and Gov, Nir S. and Yochelis, Arik},
  title     = {Why a Large-Scale Mode Can Be Essential for Understanding Intracellular Actin Waves},
  series = {Cells},
  volume    = {9},
  journal   = {Cells},
  number    = {6},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2073-4409},
  doi       = {10.3390/cells9061533},
  pages     = {18},
  year      = {2020},
  abstract  = {During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator-inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.},
  language  = {en}
}
@article{StraubePikovskij2011,
  author    = {Straube, Arthur V. and Pikovskij, Arkadij},
  title     = {Pattern formation induced by time-dependent advection},
  series = {Mathematical modelling of natural phenomena},
  volume    = {6},
  journal   = {Mathematical modelling of natural phenomena},
  number    = {1},
  publisher = {EDP Sciences},
  address   = {Les Ulis},
  issn      = {0973-5348},
  doi       = {10.1051/mmnp/20116107},
  pages     = {138 -- 148},
  year      = {2011},
  abstract  = {We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this can be explained as crossing a threshold of Turing instability due to effective increase of one of the diffusion constants.},
  language  = {en}
}
@article{StichBeta2011,
  author    = {Stich, Michael and Beta, Carsten},
  title     = {Standing waves in a complex Ginzburg-Landau equation with time-delay feedback},
  series = {Discrete and continuous dynamical systems : a journal bridging mathematics and sciences},
  journal   = {Discrete and continuous dynamical systems : a journal bridging mathematics and sciences},
  number    = {1},
  publisher = {American Institute of Mathematical Sciences},
  address   = {Springfield},
  issn      = {1078-0947},
  pages     = {1329 -- 1334},
  year      = {2011},
  abstract  = {Standing waves are studied as solutions of a complex Ginsburg-Landau equation subjected to local and global time-delay feedback terms. The onset of standing waves is studied at the instability of the homogeneous periodic solution with respect to spatially periodic perturbations. The solution of this spatiotemporal wave pattern is given and is compared to the homogeneous periodic solution.},
  language  = {en}
}