Integrated Calendar

We present a discussion of aspects of vision determined by the physics underlying our ability to perceive “non-objects”. These are astigmatic objects, including some classical anamorphisms found in curio cabinets of kings; our view of things below the surface of water, and reciprocally, a fish’s view of what is above that surface. These non-objects provide some deep insights into our binocular vision and notions of perspective. Considering the optics of the eyes that see these things, a curiosity of evolution arises in the much finer design of the fish’s eye than our own, its considerably newer successor.

I will present recent joint work with F. Rassoul-Agha (Utah) and T. Seppalainen (Madison) where we consider random walk on a hypercubic lattice of arbitrary dimension in a space-time random environment that is assumed to be temporally independent and spatially translation invariant. The large deviation principle (LDP) for the empirical velocity of the averaged walk (i.e., level-1) is simply Cramer’s theorem. We take the point of view of the particle and establish the process-level (i.e., level-3) averaged LDP for the environment Markov chain. The rate function $I_{3,a}$ is a specific relative entropy which reproduces Cramer’s rate function via the so-called contraction principle. We identify the unique minimizer of this contraction at any velocity and analyse its structure. When the environment is spatially ergodic, the level-3 quenched LDP follows from our previous work which gives a variational formula for the rate function $I_{3,q}$ involving a Donsker-Varadhan-type relative entropy $H_q$. We derive a decomposition formula for $I_{3,a}$ that expresses it as a sum of contributions from the walk (via $H_q$) and the environment. We use this formula to characterize the equality of the level-1 averaged and quenched rate functions, and conclude with several related results and open problems.

The reconstruction of thermal history is key to study the geodynamic evolution of sedimentary basins through burial, metamorphism, magmatism, deformation and exhumation. Carbonate clumped isotope thermometry enables such reconstructions in carbonate minerals, and complements ‘conventional’ low-temperature thermochronometers (e.g. apatite and zircon fission-tracks or U-Th/He systems) by constraining the peak burial temperature and the cooling rate.
Most published uses of carbonate clumped isotope thermometry aim to measure depositional temperatures of Earth-surface sedimentary carbonates. However, it has also been shown that carbonate clumped-isotope measurements of minerals formed or re-equilibrated at elevated temperatures can constrain thermal histories of sub-surface rocks. Only very recently have we had the experimental constraints on solid-state isotopic reordering to translate clumped-isotope measurements of such materials into quantitative statements about burial and exhumation. These data have led to a new generation of conceptual models describing changes in clumped-isotope composition during heating and cooling; taken together, these experiments and models enable a new approach to the study of burial, metamorphism and exhumation over long timescales and large areas. This presentation will discuss applications of this approach to constrain the thermal history of carbonate rocks exhumed in back-arc (Naxos, Greece) and mid-continental (Colorado Plateau) basins.
The exhumation of Naxos metamorphic core-complex entailed a complex thermal history, mineral-mineral and water-rock reactions, and deformation. These processes were registered in the bulk and clumped isotope composition of marbles. Calcite and dolomite marbles from Naxos show large variation of carbonate clumped-isotope values, in association with deformation and secondary mineralization fabrics. Results suggest that dynamic recrystallization of calcite can reset the carbonate clumped-isotope signal, which consequentially records the minimum temperature of dynamic recrystallization in natural samples. Carbonate clumped isotope data from the center of Naxos core-complex are consistent with the thermal history as recorded by multiple ‘conventional’ thermochronometers, but require a faster cooling rate than previously suggested, consistent with a heat shock driven by magmatic and hydrothermal activities.
Carbonate clumped isotope thermometry is used to study the burial, uplift and exhumation histories of the Colorado Plateau (USA). There, carbonate rocks were not recrystallized to marbles, and therefore their clumped isotope signals are expected to be sensitive to the peak-burial temperature. Given such constrains on the thermal history, it is straightforward to infer the thermal gradients during peak burial, and calculate total-exhumation (i.e. the volume of rock removed) in-situ. Preliminary results from the southwestern rim and the interior of the Plateau are so far consistent with published constrains on peak burial temperatures.