We consider bistable reaction-diffusion equations in funnel-shaped domains of RN made up straight parts and conical with positive opening angles. study the large time dynamics entire solutions emanating from a planar front part such domain moving into part. show dichotomy between blocking spreading, by proving especially some new Liouville type results on stable semilinear elliptic whole space ...

product innovation success has very much to do with the development of models ormetaphors that are able to guide actors. one can observe two traditions in thisregard: rational and non-rational models. apparently in the former the model, suchas “development funnel”, is regarded as a mechanism and rigid applicable, picturinginnovation as an orderly, goal-oriented, value-neutral, and systematic pr...

Funnels are a new natural subclass of DAGs. Intuitively, a DAG is a funnel if every source-sink path can be uniquely identified by one of its arcs. Funnels are an analog to trees for directed graphs that is more restrictive than DAGs but more expressive than in-/out-trees. Computational problems such as finding vertex-disjoint paths or tracking the origin of memes remain NP-hard on DAGs while o...

We present a microfluidic ratchet that exploits the deformation of individual cells through microscale funnel constrictions. The threshold pressure required to transport single cells through such constrictions is greater against the direction of taper than along the direction of taper. This physical asymmetry combined with an oscillatory excitation can enable selective and irreversible transpor...

We define a Byrnes-Isidori form for a class of infinite-dimensional systems with relative degree r and show that any system belonging to this class can be transformed into this form. We also analyze the concept of (stable) zero dynamics and show that it is, together with the Byrnes-Isidori form, instrumental for static proportional high-gain output feedback stabilization. Moreover, we show that...