The optimal driving waveform for overdamped, adiabatic rocking ratchets

The optimal driving waveform among a wide class of admissible functions for an overdamped, adiabatic rocking ratchet is shown to be dichotomous. 'Optimum' is defined as that which achieves the maximum (or minimum negative) average particle velocity. Implications for the design of ratchets, for example in nanotechnological transport, may follow. The main result is applicable to a general class of adiabatic responses. Much scope exists for further studies of ratchet waveform optimization in other regimes

Finite sampling interval effects in Kramers-Moyal analysis

Large sampling intervals can affect reconstruction of Kramers-Moyal coefficients from data. A new method, which is direct, non-stochastic and exact up to numerical accuracy, is developed to estimate these finite time effects. The method is applied numerically to biologically inspired examples. Exact finite time effects are also described analytically for two special cases. The approach developed will permit better evaluation of Langevin or Fokker-Planck based models from data with large sampling intervals. It can also be used to predict the sampling intervals for which finite time effects become significant

Geometric and projection effects in Kramers-Moyal analysis

Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze stochastic time series, particularly nonlinear ones. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically-inspired examples, these effects are predicted and explored with a non-stochastic projection operator method, and compared with direct numerical simulation of the systems' Langevin equations. General features and characteristics are identified, and the utility of the Kramers-Moyal method discussed. Projections of a system are in general non-Markovian, but here the Kramers-Moyal method remains useful, and in any case the primary examples considered are found to be close to Markovian.Comment: Submitted to Phys. Rev.

When optimization for governing human environment tipping elements is neither sustainable nor safe

Optimizing economic welfare in environmental governance has been criticized for delivering short-term gains at the expense of long-term environmental degradation. Different from economic optimization, the concepts of sustainability and the more recent safe operating space have been used to derive policies in environmental governance. However, a formal comparison between these three policy paradigms is still missing, leaving policy makers uncertain which paradigm to apply. Here, we develop a better understanding of their interrelationships, using a stylized model of human-environment tipping elements. We find that no paradigm guarantees fulfilling requirements imposed by another paradigm and derive simple heuristics for the conditions under which these trade-offs occur. We show that the absence of such a master paradigm is of special relevance for governing real-world tipping systems such as climate, fisheries, and farming, which may reside in a parameter regime where economic optimization is neither sustainable nor safe.The authors are grateful for financial support from the Heinrich-Böll-Foundation, the Stordalen Foundation (via the Planetary Boundaries Research Network PB.net), the Earth League’s EarthDoc program, the Leibniz Association (project DOMINOES) and the Swedish Research Council Formas (Project Grant 2014-589)

Resilience as pathway diversity: Linking systems, individual, and temporal perspectives on resilience

Approaches to understanding resilience from psychology and sociology emphasize individuals' agency but obscure systemic factors. Approaches to understanding resilience stemming from ecology emphasize system dynamics such as feedbacks but obscure individuals. Approaches from both psychology and ecology examine the actions or attractors available in the present, but neglect how actions taken now can affect the configuration of the social-ecological system in the future. Here, we propose an extension to resilience theory, which we label "pathway diversity", that links existing individual, systems, and temporal theories of resilience into a common framework. In our theory of pathway diversity, resilience is greater if more actions are currently available and can be maintained or enhanced into the future. Using a stylized model of an agricultural social-ecological system, we show how pathway diversity could deliver a context-sensitive method of assessing resilience and guiding planning. Using a stylized state-and-transition model of a poverty trap, we show how pathway diversity is generally consistent with existing definitions of resilience and can illuminate long-standing questions about normative and descriptive resilience. Our results show that pathway diversity advances both theoretical understanding and practical tools for building resilience.The research leading to these results has received funding from the Swedish Research Council Formas (grant 2014-589)

Finite sampling interval effects in Kramers-Moyal analysis

Large sampling intervals can affect reconstruction of Kramers-Moyal coefficients from data. A new method, which is direct, non-stochastic and exact up to numerical accuracy, can estimate these finite-time effects. For the first time, exact finite-time effects are described analytically for special cases; biologically inspired numerical examples are also worked through numerically. The approach developed here will permit better evaluation of Langevin or Fokker-Planck based models from data with large sampling intervals. It can also be used to predict the sampling intervals for which finite-time effects become significant.Comment: Preprin