(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

A new scenario framework for climate change research: background, process, and future directions

The scientific community is developing new global, regional, and sectoral scenarios to facilitate interdisciplinary research and assessment to explore the range of possible future climates and related physical changes that could pose risks to human and natural systems; how these changes could interact with social, economic, and environmental development pathways; the degree to which mitigation and adaptation policies can avoid and reduce risks; the costs and benefits of various policy mixes; residual impacts under alternative pathways; and the relationship of future climate change and adaptation and mitigation policy responses with sustainable development. This paper provides the background to and process of developing the conceptual framework for these scenarios, as described in the three subsequent papers in this Special Issue (Van Vuuren et al.; O’Neill et al.; Kriegler et al.). The paper also discusses research needs to further develop and apply this framework. A key goal of the current framework design and its future development is to facilitate the collaboration of climate change researchers from a broad range of perspectives and disciplines to develop policy- and decision-relevant scenarios and explore the challenges and opportunities human and natural systems could face with additional climate change.