Oscillators and relaxation phenomena in Pleistocene climate theory

Ice sheets appeared in the northern hemisphere around 3 million years ago and glacial-interglacial cycles have paced Earth's climate since then. Superimposed on these long glacial cycles comes an intricate pattern of millennial and sub-millennial variability, including Dansgaard-Oeschger and Heinrich events. There are numerous theories about theses oscillations. Here, we review a number of them in order to draw a parallel between climatic concepts and dynamical system concepts, including, in particular, the relaxation oscillator, excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all theories of ice ages reviewed here feature a phenomenon of synchronisation between internal climate dynamics and the astronomical forcing. However, these theories differ in their bifurcation structure and this has an effect on the way the ice age phenomenon could grow 3 million years ago. All theories on rapid events reviewed here rely on the concept of a limit cycle in the ocean circulation, which may be excited by changes in the surface freshwater surface balance. The article also reviews basic effects of stochastic fluctuations on these models, including the phenomenon of phase dispersion, shortening of the limit cycle and stochastic resonance. It concludes with a more personal statement about the potential for inference with simple stochastic dynamical systems in palaeoclimate science. Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages, Dansgaard-Oeschger eventsComment: Published in the Transactions of the Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), as a contribution to the Proceedings of the workshop on Stochastic Methods in Climate Modelling, Newton Institute (23-27 August). Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on request to author and on http://www.uclouvain.be/ito

Elevated atmospheric sulfur levels off the Peruvian coast

Elevated levels of non‐sea‐salt sulfate and SO2 in samples collected off the west coast of South America indicate that there is a major source of atmospheric sulfur in the region of southern Peru and northern Chile. During a 1983 cruise, observed concentrations of non‐sea‐salt sulfur, SO2, selenium, arsenic, and antimony were comparable to levels reported for moderately polluted urban air. In contrast, methanesulfonic acid levels were typical of coastal marine air. Clearly, the elevated atmospheric sulfur levels in this region cannot be ascribed to oceanic organosulfur emissions. The major inputs are tentatively attributed to the smelting of sulfide ores which is a major industry in this region. The transport of smelter derived aerosols to this region may have a number of consequences for the atmospheric and oceanic chemistry of the Peruvian upwelling area

Transitions across Melancholia States in a climate model: reconciling the deterministic and stochastic points of view

The Earth is well known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realized. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a result of the positive ice-albedo feedback. In a previous investigation performed on a intermediate complexity climate model we identified the unstable climate states (melancholia states) separating the coexisting climates, and studied their dynamical and geometrical properties. The melancholia states are ice covered up to the midlatitudes and attract trajectories initialized on the basin boundary. In this Letter, we study how stochastically perturbing the parameter controlling the intensity of the incoming solar radiation impacts the stability of the climate. We detect transitions between the warm and the snowball state and analyze in detail the properties of the noise-induced escapes from the corresponding basins of attraction. We determine the most probable paths for the transitions and find evidence that the melancholia states act as gateways, similarly to saddle points in an energy landscape

Estimation of bubble-mediated air–sea gas exchange from concurrent DMS and CO2 transfer velocities at intermediate–high wind speeds

Simultaneous air–sea fluxes and concentration differences of dimethylsulfide (DMS) and carbon dioxide (CO2) were measured during a summertime North Atlantic cruise in 2011. This data set reveals significant differences between the gas transfer velocities of these two gases (Δkw) over a range of wind speeds up to 21 m s−1. These differences occur at and above the approximate wind speed threshold when waves begin breaking. Whitecap fraction (a proxy for bubbles) was also measured and has a positive relationship with Δkw, consistent with enhanced bubble-mediated transfer of the less soluble CO2 relative to that of the more soluble DMS. However, the correlation of Δkw with whitecap fraction is no stronger than with wind speed. Models used to estimate bubble-mediated transfer from in situ whitecap fraction underpredict the observations, particularly at intermediate wind speeds. Examining the differences between gas transfer velocities of gases with different solubilities is a useful way to detect the impact of bubble-mediated exchange. More simultaneous gas transfer measurements of different solubility gases across a wide range of oceanic conditions are needed to understand the factors controlling the magnitude and scaling of bubble-mediated gas exchange

On the Hyperbolicity of Lorenz Renormalization

We consider infinitely renormalizable Lorenz maps with real critical exponent $\alpha>1$ and combinatorial type which is monotone and satisfies a long return condition. For these combinatorial types we prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated unstable manifold. An unstable manifold defines a family of Lorenz maps and we prove that each infinitely renormalizable combinatorial type (satisfying the above conditions) has a unique representative within such a family. We also prove that each infinitely renormalizable map has no wandering intervals and that the closure of the forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure

Nonlinear rheology of colloidal dispersions

Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.Comment: Review articl

Driven diffusion in a periodically compartmentalized tube: homogeneity versus intermittency of particle motion

We study the effect of a driving force F on drift and diffusion of a point Brownian particle in a tube formed by identical ylindrical compartments, which create periodic entropy barriers for the particle motion along the tube axis. The particle transport exhibits striking features: the effective mobility monotonically decreases with increasing F, and the effective diffusivity diverges as F → ∞, which indicates that the entropic effects in diffusive transport are enhanced by the driving force. Our consideration is based on two different scenarios of the particle motion at small and large F, homogeneous and intermittent, respectively. The scenarios are deduced from the careful analysis of statistics of the particle transition times between neighboring openings. From this qualitative picture, the limiting small-F and large-F behaviors of the effective mobility and diffusivity are derived analytically. Brownian dynamics simulations are used to find these quantities at intermediate values of the driving force for various compartment lengths and opening radii. This work shows that the driving force may lead to qualitatively different anomalous transport features, depending on the geometry design

Yours ever (well, maybe): Studies and signposts in letter writing

Electronic mail and other digital communications technologies seemingly threaten to end the era of handwritten and typed letters, now affectionately seen as part of snail mail. In this essay, I analyze a group of popular and scholarly studies about letter writing-including examples of pundits critiquing the use of e-mail, etiquette manuals advising why the handwritten letter still possesses value, historians and literary scholars studying the role of letters in the past and what it tells us about our present attitudes about digital communications technologies, and futurists predicting how we will function as personal archivists maintaining every document including e-mail. These are useful guideposts for archivists, providing both a sense of the present and the past in the role, value and nature of letters and their successors. They also provide insights into how such documents should be studied, expanding our gaze beyond the particular letters, to the tools used to create them and the traditions dictating their form and function. We also can discern a role for archivists, both for contributing to the literature about documents and in using these studies and commentaries, suggesting not a new disciplinary realm but opportunities for new interdisciplinary work. Examining a documentary form makes us more sensitive to both the innovations and traditions as it shifts from the analog to the digital; we can learn not to be caught up in hysteria or nostalgia about one form over another and archivists can learn about what they might expect in their labors to document society and its institutions. At one time, paper was part of an innovative technology, with roles very similar to the Internet and e-mail today. It may be that the shifts are far less revolutionary than is often assumed. Reading such works also suggests, finally, that archivists ought to rethink how they view their own knowledge and how it is constructed and used. © 2010 Springer Science+Business Media B.V