Symmetric hyperbolic systems for Bianchi equations

We obtain a family of first-order symmetric hyperbolic systems for the Bianchi equations. They have only physical characteristics: the light cone and timelike hypersurfaces. In the proof of the hyperbolicity, new positivity properties of the Bel tensor are used.Comment: latex, 7 pages, accepted for publication in Class. Quantum Gra

The competing impacts of climate change and nutrient reductions on dissolved oxygen in Chesapeake Bay

The Chesapeake Bay region is projected to experience changes in temperature, sea level, and precipitation as a result of climate change. This research uses an estuarine-watershed hydrodynamic-biogeochemical modeling system along with projected mid-21st-century changes in temperature, freshwater flow, and sea level rise to explore the impact climate change may have on future Chesapeake Bay dissolved-oxygen (DO) concentrations and the potential success of nutrient reductions in attaining mandated estuarine water quality improvements. Results indicate that warming bay waters will decrease oxygen solubility year-round, while also increasing oxygen utilization via respiration and remineralization, primarily impacting bottom oxygen in the spring. Rising sea level will increase estuarine circulation, reducing residence time in bottom waters and increasing stratification. As a result, oxygen concentrations in bottom waters are projected to increase, while oxygen concentrations at mid-depths (3 \u3c DO \u3c 5 mg L-1) will typically decrease. Changes in precipitation are projected to deliver higher winter and spring freshwater flow and nutrient loads, fueling increased primary production. Together, these multiple climate impacts will lower DO throughout the Chesapeake Bay and negatively impact progress towards meeting water quality standards associated with the Chesapeake Bay Total Maximum Daily Load. However, this research also shows that the potential impacts of climate change will be significantly smaller than improvements in DO expected in response to the required nutrient reductions, especially at the anoxic and hypoxic levels. Overall, increased temperature exhibits the strongest control on the change in future DO concentrations, primarily due to decreased solubility, while sea level rise is expected to exert a small positive impact and increased winter river flow is anticipated to exert a small negative impact

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio

Ultracoherence and Canonical Transformations

The (in)finite dimensional symplectic group of homogeneous canonical transformations is represented on the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states.Comment: 24 page

On hybrid states of two and three level atoms

We calculate atom-photon resonances in the Wigner-Weisskopf model, admitting two photons and choosing a particular coupling function. We also present a rough description of the set of resonances in a model for a three-level atom coupled to the photon field. We give a general picture of matter-field resonances these results fit into.Comment: 33 pages, 12 figure

Sediment Delivery to a Tidal Marsh Platform Is Minimized by Source Decoupling and Flux Convergence

Sediment supply is a primary factor in determining marsh response to sea level rise and is typically approximated through high‐resolution measurements of suspended sediment concentrations (SSCs) from adjacent tidal channels. However, understanding sediment transport across the marsh itself remains limited by discontinuous measurements of SSC over individual tidal cycles. Here, we use an array of optical turbidity sensors to build a long‐term, continuous record of SSC across a marsh platform and adjacent tidal channel. We find that channel and marsh concentrations are correlated (i.e., coupled) within tidal cycles but are largely decoupled over longer time scales. We also find that net sediment fluxes decline to near zero within 10 m of the marsh edge. Together, these results suggest that large sections of the marsh platform receive minimal sediment independent of flooding frequency or channel sediment supply. Marsh‐centric, as opposed to channel‐centric, measures of sediment supply may better characterize marsh platform vulnerability

Estuarine Dissolved Organic Carbon Flux From Space: With Application to Chesapeake and Delaware Bays

This study uses a neural network model trained with in situ data, combined with satellite data and hydrodynamic model products, to compute the daily estuarine export of dissolved organic carbon (DOC) at the mouths of Chesapeake Bay (CB) and Delaware Bay (DB) from 2007 to 2011. Both bays show large flux variability with highest fluxes in spring and lowest in fall as well as interannual flux variability (0.18 and 0.27 Tg C/year in 2008 and 2010 for CB; 0.04 and 0.09 Tg C/year in 2008 and 2011 for DB). Based on previous estimates of total organic carbon (TOCexp) exported by all Mid‐Atlantic Bight estuaries (1.2 Tg C/year), the DOC export (CB + DB) of 0.3 Tg C/year estimated here corresponds to 25% of the TOCexp. Spatial and temporal covariations of velocity and DOC concentration provide contributions to the flux, with larger spatial influence. Differences in the discharge of fresh water into the bays (74 billion m3/year for CB and 21 billion m3/year for DB) and their geomorphologies are major drivers of the differences in DOC fluxes for these two systems. Terrestrial DOC inputs are similar to the export of DOC at the bay mouths at annual and longer time scales but diverge significantly at shorter time scales (days to months). Future efforts will expand to the Mid‐Atlantic Bight and Gulf of Maine, and its major rivers and estuaries, in combination with coupled terrestrial‐estuarine‐ocean biogeochemical models that include effects of climate change, such as warming and CO2 increase

On 2D Viscoelasticity with Small Strain

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.Comment: Different contributions of strain and rotation of the deformation are studied for viscoelastic fluids of Oldroyd-B type in 2

Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Our software---CHUNKYEuler---is available as open source on Bitbucket. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams