The Complete Jamming Landscape of Confined Hard Discs

An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $\sigma$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/\sigma < 2$. By considering all possible local packing arrangements, the generalized ensemble partition function of jammed states is obtained using the transfer matrix method, which allows us to calculate the configurational entropy and the equation of state for the packings. Exploring the relationship between structural order and packing density, we find that the geometric frustration between local packing environments plays an important role in determining the density distribution of jammed states and that structural "randomness" is a non-monotonic function of packing density. Molecular dynamics simulations show that the properties of the equilibrium liquid are closely related to those of the landscape.Comment: 5 Pages, 4 figure

State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes

Equilibrium climate sensitivity (ECS) is a key predictor of climate change. However, it is not very well constrained, either by climate models or by observational data. The reasons for this include strong internal variability and forcing on many time scales. In practise this means that the 'equilibrium' will only be relative to fixing the slow feedback processes before comparing palaeoclimate sensitivity estimates with estimates from model simulations. In addition, information from the late Pleistocene ice age cycles indicates that the climate cycles between cold and warm regimes, and the climate sensitivity varies considerably between regime because of fast feedback processes changing relative strength and time scales over one cycle. In this paper we consider climate sensitivity for quite general climate dynamics. Using a conceptual Earth system model of Gildor and Tziperman (2001) (with Milankovich forcing and dynamical ocean biogeochemistry) we explore various ways of quantifying the state-dependence of climate sensitivity from unperturbed and perturbed model time series. Even without considering any perturbations, we suggest that climate sensitivity can be usefully thought of as a distribution that quantifies variability within the 'climate attractor' and where there is a strong dependence on climate state and more specificially on the 'climate regime' where fast processes are approximately in equilibrium. We also consider perturbations by instantaneous doubling of CO$_2$ and similarly find a strong dependence on the climate state using our approach.Comment: 32 pages, 10 figure

Extreme sensitivity and climate tipping points

A climate state close to a tipping point will have a degenerate linear response to perturbations, which can be associated with extreme values of the equilibrium climate sensitivity (ECS). In this paper we contrast linearized (`instantaneous') with fully nonlinear geometric (`two-point') notions of ECS, in both presence and absence of tipping points. For a stochastic energy balance model of the global mean surface temperature with two stable regimes, we confirm that tipping events cause the appearance of extremes in both notions of ECS. Moreover, multiple regimes with different mean sensitivities are visible in the two-point ECS. We confirm some of our findings in a physics-based multi-box model of the climate system.Comment: 11 figure