Several phenomena can be described by a number of densities (of mass, population, probability, ...) distributed in a domain and subject to di↵usion, reaction, and either cooperative or competitive interaction. Whenever the interaction is the prevailing mechanism, one can reasonably expect pattern formation and, in the competitive case, that the several densities can not coexist and tend to segr...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. Depending on driving conditions, step bunching and meandering, mound formation, or surface smoothening may be seen in the presence of a kinetic asymmetry at the steps or kinks. We employ a step model to calculate the induced mass flux along misoriented surfaces, which accounts for surface dynam...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

We study the effects of adding a local perturbation in a pattern forming system, taking as an example the Ginzburg-Landau equation with a small localized inhomogeneity in two dimensions. Measuring the response through the linearization at a periodic pattern, one finds an unbounded linear operator that is not Fredholm due to continuous spectrum in typical translation invariant or weighted spaces...

where ∆ denotes a diffusion operator, is central to many biological applications, in fields ranging from pattern formation in development to ecology. One of the central topics of research in this context is the question of how the stability of solutions of the PDE relates to stability of solutions of the underlying ordinary differential equation (ODE) dx dt (t) = F (x(t), t). This paper shows t...

The conditions for macroscopic segregation of A and B in a steady-state A + B ---, 0 reaction are studied in infinite systems. Segregation occurs in one and two dimensions and is marginal for d = 3. We note the dependence of these results on the precise experimental conditions assumed in the theory. We also note the difference between these results and our earlier ones for finite systems where ...

Here we investigate how development and evolution can affect each other by exploring what kind of phenotypic variation is produced by different types of developmental mechanisms. A limited number of developmental mechanisms are capable of pattern formation in development. Two main types have been identified. In morphodynamic mechanisms, induction events and morphogenetic processes, such as simp...

Pattern formation is a phenomenon that arises in a wide variety of physical, chemical and biological situations. A great deal of theoretical progress has been made in understanding the universal aspects of pattern formation in terms of amplitudes of the modes that make up the pattern. Much of the theory has sound mathematical justification, but experiments and numerical simulations over the las...

Article history: Received 3 November 2010 Revised 4 March 2011 Available online 24 March 2011 MSC: 35K57 35B36 35B32 92D40