Time-dependent rotational stability of dynamic planets with elastic lithospheres

True polar wander (TPW), a reorientation of the rotation axis relative to the solid body, is driven by mass redistribution on the surface or within the planet and is stabilized by two aspects of the planet's viscoelastic response: the delayed viscous readjustment of the rotational bulge and the elastic stresses in the lithosphere. The latter, following Willemann (1984), is known as remnant bulge stabilization. In the absence of a remnant bulge, the rotation of a terrestrial planet is said to be inherently unstable. Theoretical treatments have been developed to treat the final (equilibrium) state in this case and the time-dependent TPW toward this state, including nonlinear approaches that assume slow changes in the inertia tensor. Moreover, remnant bulge stabilization has been incorporated into both equilibrium and linearized, time-dependent treatments of rotational stability. We extend the work of Ricard et al. (1993) to derive a nonlinear, time-dependent theory of TPW that incorporates stabilization by both the remnant bulge and viscous readjustment of the rotational bulge. We illustrate the theory using idealized surface loading scenarios applied to models of both Earth and Mars. We demonstrate that the inclusion of remnant bulge stabilization reduces both the amplitude and timescale of TPW relative to calculations in which this stabilization is omitted. Furthermore, given current estimates of mantle viscosity for both planets, our calculations indicate that departures from the equilibrium orientation of the rotation axis in response to forcings with timescale of 1 Myr or greater are significant for Earth but negligible for Mars

Sources of nonlinearities, chatter generation and suppression in metal cutting

The mechanics of chip formation has been revisited in order to understand functional relationships between the process and the technological parameters. This has led to the necessity of considering the chip-formation process as highly nonlinear, with complex interrelations between its dynamics and thermodynamics. In this paper a critical review of the state of the art of modelling and the experimental investigations is outlined with a view to how the nonlinear dynamics perception can help to capture the major phenomena causing instabilities (chatter) in machining operations. The paper is concluded with a case study, where stability of a milling process is investigated in detail, using an analytical model which results in an explicit relation for the stability limit. The model is very practical for the generation of the stability lobe diagrams, which is time consuming when using numerical methods. The extension of the model to the stability analysis of variable pitch cutting tools is also given. The application and verification of the method are demonstrated by several examples

Snowball Earth climate dynamics and Cryogenian geology-geobiology

Geological evidence indicates that grounded ice sheets reached sea level at all latitudes during two long-lived Cryogenian (58 and ≥5 My) glaciations. Combined uranium-lead and rhenium-osmium dating suggests that the older (Sturtian) glacial onset and both terminations were globally synchronous. Geochemical data imply that CO2 was 102 PAL (present atmospheric level) at the younger termination, consistent with a global ice cover. Sturtian glaciation followed breakup of a tropical supercontinent, and its onset coincided with the equatorial emplacement of a large igneous province. Modeling shows that the small thermal inertia of a globally frozen surface reverses the annual mean tropical atmospheric circulation, producing an equatorial desert and net snow and frost accumulation elsewhere. Oceanic ice thickens, forming a sea glacier that flows gravitationally toward the equator, sustained by the hydrologic cycle and by basal freezing and melting. Tropical ice sheets flow faster as CO2 rises but lose mass and become sensitive to orbital changes. Equatorial dust accumulation engenders supraglacial oligotrophic meltwater ecosystems, favorable for cyanobacteria and certain eukaryotes. Meltwater flushing through cracks enables organic burial and submarine deposition of airborne volcanic ash. The subglacial ocean is turbulent and well mixed, in response to geothermal heating and heat loss through the ice cover, increasing with latitude. Terminal carbonate deposits, unique to Cryogenian glaciations, are products of intense weathering and ocean stratification. Whole-ocean warming and collapsing peripheral bulges allow marine coastal flooding to continue long after ice-sheet disappearance. The evolutionary legacy of Snowball Earth is perceptible in fossils and living organisms

Orbitally forced ice sheet fluctuations during the Marinoan Snowball Earth glaciation

Two global glaciations occurred during the Neoproterozoic. Snowball Earth theory posits that these were terminated after millions of years of frigidity when initial warming from rising atmospheric CO2 concentrations was amplified by the reduction of ice cover and hence a reduction in planetary albedo. This scenario implies that most of the geological record of ice cover was deposited in a brief period of melt-back. However, deposits in low palaeo-latitudes show evidence of glacial–interglacial cycles. Here we analyse the sedimentology and oxygen and sulphur isotopic signatures of Marinoan Snowball glaciation deposits from Svalbard, in the Norwegian High Arctic. The deposits preserve a record of oscillations in glacier extent and hydrologic conditions under uniformly high atmospheric CO2 concentrations. We use simulations from a coupled three-dimensional ice sheet and atmospheric general circulation model to show that such oscillations can be explained by orbital forcing in the late stages of a Snowball glaciation. The simulations suggest that while atmospheric CO2 concentrations were rising, but not yet at the threshold required for complete melt-back, the ice sheets would have been sensitive to orbital forcing. We conclude that a similar dynamic can potentially explain the complex successions observed at other localities

The quantification of COMT mRNA in post mortem cerebellum tissue: diagnosis, genotype, methylation and expression

BACKGROUND: The COMT gene is located on chromosome 22q11, a region strongly implicated in the aetiology of several psychiatric disorders, in particular schizophrenia. Previous research has suggested that activity and expression of COMT is altered in schizophrenia, and is mediated by one or more polymorphisms within the gene, including the functional Val(158)Met polymorphism. METHOD: In this study we examined the expression levels of COMT mRNA using quantitative RT-PCR in 60 post mortem cerebellum samples derived from individuals with schizophrenia, bipolar disorder, depression, and no history of psychopathology. Furthermore, we have examined the methylation status of two CpG sites in the promoter region of the gene. RESULTS: We found no evidence of altered COMT expression or methylation in any of the psychiatric diagnoses examined. We did, however, find evidence to suggest that genotype is related to COMT gene expression, replicating the findings of two previous studies. Specifically, val(158)met (rs165688; Val allele) rs737865 (G allele) and rs165599 (G allele) all showed reduced expression (P < 0.05). Finally, we observe a strong sexual dimorphism in COMT expression, with females exhibiting significantly greater levels of COMT mRNA. CONCLUSION: The expression of COMT does not appear to be altered in the cerebellum of individuals suffering from schizophrenia, bipolar disorder or depression, but does appear to be influenced by single nucleotide polymorphisms within the gene