Freidlin-Wentzell theory of large deviations for the description of the effect of small random perturbations on dynamical systems is exploited as a numerical tool. Specifically, a numerical algorithm is proposed to compute the quasipotential in the theory, which is the key object to quantify the dynamics on long time scales when the effect of the noise becomes ubiquitous: the equilibrium distribution of the system, the pathways of transition between metastable states and their rate, etc., can all be expressed in terms of the quasi-potential. We propose an algorithm to compute these quantities called the geometric minimum action method (gMAM), which is a blend of the original minimum action method (MAM) and the string method. It is based on a reformulation of the large deviations action functional on the space of curves that allows one to easily perform the double minimization of the original action required to compute the quasi-potential. The theoretical background of the gMAM in the context of large deviations theory is discussed in detail, as well as the algorithmic aspects of the method. The gMAM is then illustrated on several examples: a finite-dimensional system displaying bistability and modeled by a nongradient stochastic ordinary differential equation, an infinite-dimensional analogue of this system modeled by a stochastic partial differential equation, and an example of a bistable genetic switch modeled by a Markov jump process.

Even in nonequilibrium systems, the mechanism of rare reactive events caused by small random noise is predictable because they occur with high probability via their maximum likelihood path (MLP). Here a geometric characterization of the MLP is given as the curve minimizing a certain functional under suitable constraints. A general purpose algorithm is also proposed to compute the MLP. This algorithm is applied to predict the pathway of transition in a bistable stochastic reaction-diffusion equation in the presence of a shear flow, and to analyze how the shear intensity influences the mechanism and rate of the transition.

An algorithm is proposed to calculate the minimum energy path (MEP). The algorithm is based on a variational formulation in which the MEP is characterized as the curve minimizing a certain functional. The algorithm performs this minimization using a preconditioned steepest-descent scheme with a reparametrization step to enforce a constraint on the curve parametrization.

Ideas and knowledge about climate have changed considerably in history. Ancient philosophers like Hippocrates and Aristotle shaped the understandings of climate, which remained very influential until well into the eighteenth century. The Scientific Revolution of the seventeenth century gave rise to new ways of systematic instrument-based observation of and increased public interest in weather and climate. These developments led to a mechanistic understanding and a reductionist physical description of climate in the twentieth century, eventually in the form of a complex earth system. Furthermore, different understandings of climate coexisted in many periods of time. Only in the nineteenth and twentieth centuries specific scientific concepts of climate (a geographical understanding of climate in climatology until about the mid-twentieth century and a physical understanding of climate in climate science in the second half of the twentieth century) gained superior social credibility and cultural dominance. The understanding of climate involved more than the accumulation of scientific knowledge. It was rooted in social processes and cultural interests, which shaped different ideas of climate in different communities of actors and different historical times .  2010 John Wiley & Sons, Ltd. WIREs Clim Change 2010 1 581-597 'Ideas on climate change are changing faster than climate itself' [1, p. 257].

No abstract