A Corollary for Nonsmooth Systems

In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are developed using differential inclusions to achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function

Sulfate Burial Constraints on the Phanerozoic Sulfur Cycle

The sulfur cycle influences the respiration of sedimentary organic matter, the oxidation state of the atmosphere and oceans, and the composition of seawater. However, the factors governing the major sulfur fluxes between seawater and sedimentary reservoirs remain incompletely understood. Using macrostratigraphic data, we quantified sulfate evaporite burial fluxes through Phanerozoic time. Approximately half of the modern riverine sulfate flux comes from weathering of recently deposited evaporites. Rates of sulfate burial are unsteady and linked to changes in the area of marine environments suitable for evaporite formation and preservation. By contrast, rates of pyrite burial and weathering are higher, less variable, and largely balanced, highlighting a greater role of the sulfur cycle in regulating atmospheric oxygen

Exponential decay in a spin bath

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.Comment: 4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices with extensive technical details, version to appear in Phys. Rev. B

Current-eddy interaction in the Agulhas Return Current region from the seismic oceanography perspective

Interleaving in the Agulhas Return Current (ARC) frontal region is commonly manifested in the form of thermohaline intrusions, as sub-tropical and sub-polar water masses of similar density meet. In Jan/Feb 2012, the Naval Research Laboratory and collaborators carried out a field experiment in which seismic and traditional hydrographic observations were acquired to examine frontal zone mixing processes. The high lateral resolution (10 m) of the seismic observations allowed fine-scale lateral tracking of thermal intrusions, which were corroborated with simultaneous XBT casts. Between seismic deployments both salinity and temperature data were acquired via CTD, Underway-CTD and microstructure profiles. This study focuses on analyzing seismic reflection data in a particular E-W transect where the northward flowing ARC interacted with the southward flowing portion of a large anticyclonic eddy. Strong reflectors were most prominent at the edge of a hyperbolic zone formed between the eddy and ARC, where sub-polar waters interacted with waters of sub-tropical origin on either side. Reflectors were shallow within the hyperbolic zone and extended to 1200 m below the ARC. The nature of the observed reflectors will be determined from comparison of seismic reflection and derived ∂T/∂z fields, and XBT and TS profiles from the available hydrographic data

Speed Limits in General Relativity

Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994) in the absence of exotic matter.Comment: 7 pages; AMS-LaTeX; accepted for publication by Classical and Quantum Gravit

Climate change and the selective signature of the Late Ordovician mass extinction

Selectivity patterns provide insights into the causes of ancient extinction events. The Late Ordovician mass extinction was related to Gondwanan glaciation; however, it is still unclear whether elevated extinction rates were attributable to record failure, habitat loss, or climatic cooling. We examined Middle Ordovician-Early Silurian North American fossil occurrences within a spatiotemporally explicit stratigraphic framework that allowed us to quantify rock record effects on a per-taxon basis and assay the interplay of macrostratigraphic and macroecological variables in determining extinction risk. Genera that had large proportions of their observed geographic ranges affected by stratigraphic truncation or environmental shifts at the end of the Katian stage were particularly hard hit. The duration of the subsequent sampling gaps had little effect on extinction risk, suggesting that this extinction pulse cannot be entirely attributed to rock record failure; rather, it was caused, in part, by habitat loss. Extinction risk at this time was also strongly influenced by the maximum paleolatitude at which a genus had previously been sampled, a macroecological trait linked to thermal tolerance. A model trained on the relationship between 16 explanatory variables and extinction patterns during the early Katian interval substantially underestimates the extinction of exclusively tropical taxa during the late Katian interval. These results indicate that glacioeustatic sea-level fall and tropical ocean cooling played important roles in the first pulse of the Late Ordovician mass extinction in Laurentia

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

A major regional air pollution event in the northeastern United States caused by extensive forest fires in Quebec, Canada

During early July 2002, wildfires burned ∼1 × 106 ha of forest in Quebec, Canada. The resultant smoke plume was seen in satellite images blanketing the U.S. east coast. Concurrently, extremely high CO mixing ratios were observed at the Atmospheric Investigation, Regional Modeling, Analysis and Prediction (AIRMAP) network sites in New Hampshire and at the Harvard Forest Environmental Measurement Site (HFEMS) in Massachusetts. The CO enhancements were on the order of 525–1025 ppbv above low mixing ratio conditions on surrounding days. A biomass burning source for the event was confirmed by concomitant enhancements in aerosol K+, NH4+, NO3−, and C2O42− mixing ratios at the AIRMAP sites. Additional data for aerosol K, organic carbon, and elemental carbon from the Interagency Monitoring of Protected Visual Environments network and CO data from Environmental Protection Agency sites indicated that the smoke plume impacted much of the U.S. east coast, from Maine to Virginia. CO mixing ratios and K concentrations at stations with 10-year or longer records suggested that this was the largest biomass burning plume to impact the U.S. east coast in over a decade. Furthermore, CO mixing ratios and aerosol particles with diameters 2.5) mass and scattering coefficients from the AIRMAP network and HFEMS indicated that this event was comparable to the large anthropogenic combustion and haze events which intermittently impact rural New England. The degree of enhancement of O3, NOy, NO3−, NH4+, and SO42− in the biomass plume showed significant variation with elevation and latitude that is attributed to variations in transport and surface depositional processes

Small-Angle Excess Scattering: Glassy Freezing or Local Orientational Ordering?

We present Monte Carlo simulations of a dense polymer melt which shows glass-transition-like slowing-down upon cooling, as well as a build up of nematic order. At small wave vectors q this model system shows excess scattering similar to that recently reported for light-scattering experiments on some polymeric and molecular glass-forming liquids. For our model system we can provide clear evidence that this excess scattering is due to the onset of short-range nematic order and not directly related to the glass transition.Comment: 3 Pages of Latex + 4 Figure