Tannakian approach to linear differential algebraic groups

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.Comment: 31 pages; corrected misprint

In-vivo magnetic resonance imaging of hyperpolarized silicon particles

Silicon-based micro and nanoparticles have gained popularity in a wide range of biomedical applications due to their biocompatibility and biodegradability in-vivo, as well as a flexible surface chemistry, which allows drug loading, functionalization and targeting. Here we report direct in-vivo imaging of hyperpolarized 29Si nuclei in silicon microparticles by MRI. Natural physical properties of silicon provide surface electronic states for dynamic nuclear polarization (DNP), extremely long depolarization times, insensitivity to the in-vivo environment or particle tumbling, and surfaces favorable for functionalization. Potential applications to gastrointestinal, intravascular, and tumor perfusion imaging at sub-picomolar concentrations are presented. These results demonstrate a new background-free imaging modality applicable to a range of inexpensive, readily available, and biocompatible Si particles.Comment: Supplemental Material include

Assessments of Composite and Discrete Sampling Approaches for Water Quality Monitoring

peer-reviewedAchieving an operational compromise between spatial coverage and temporal resolution in national scale river water quality monitoring is a major challenge for regulatory authorities, particularly where chemical concentrations are hydrologically dependent. The efficacy of flow-weighted composite sampling (FWCS) approaches for total phosphorus (TP) sampling (n = 26–52 analysed samples per year), previously applied in monitoring programmes in Norway, Sweden and Denmark, and which account for low to high flow discharges, was assessed by repeated simulated sampling on high resolution TP data. These data were collected in three research catchments in Ireland over the period 2010–13 covering a base-flow index range of 0.38 to 0.69. Comparisons of load estimates were also made with discrete (set time interval) daily and sub-daily sampling approaches (n = 365 to >1200 analysed samples per year). For all years and all sites a proxy of the Norwegian sampling approach, which is based on re-forecasting discharge for each 2-week deployment, proved most stable (median TP load estimates of 87–98%). Danish and Swedish approaches, using long-term flow records to set a flow constant, were only slightly less effective (median load estimates of 64–102% and 80–96%, respectively). Though TP load estimates over repeated iterations were more accurate using the discrete approaches, particularly the 24/7 approach (one sample every 7 h in a 24 bottle sampler - median % load estimates of 93–100%), composite load estimates were more stable, due to the integration of multiple small samples (n = 100–588) over a deployment

Configuration development study of the X-24C hypersonic research airplane

Bottom line results were made of a three-phase study to determine the feasibility of designing, building, and operating, and maintaining an air-launched high performance aircraft capable of cruising at speeds up to Mach 8 for short durations. The results show that Lockalloy heat-sink structure affords the capability for a 'work-horse' vehicle which can serve as an excellent platform for this research. It was further concluded that the performance of a blended wing body configuration surpassed that of a lifting body design for typical X-24C missions. The cost of a two vehicle program, less engines, B-52 modification and contractor support after delivery, can be kept within $70M (in Jan. 1976 dollars)

Divergences in the Effective Action for Acausal Spacetimes

The 1--loop effective Lagrangian for a massive scalar field on an arbitrary causality violating spacetime is calculated using the methods of Euclidean quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and twisted field configurations are also considered. In general, we find that the Lagrangian diverges to minus infinity at each of the nth polarised hypersurfaces of the spacetime with a structure governed by a DeWitt-Schwinger type expansion.Comment: 17 pages, Late

Models for Chronology Selection

In this paper, we derive an expression for the grand canonical partition function for a fluid of hot, rotating massless scalar field particles in the Einstein universe. We consider the number of states with a given energy as one increases the angular momentum so that the fluid rotates with an increasing angular velocity. We find that at the critical value when the velocity of the particles furthest from the origin reaches the speed of light, the number of states tends to zero. We illustrate how one can also interpret this partition function as the effective action for a boosted scalar field configuration in the product of three dimensional de Sitter space and $S^1$. In this case, we consider the number of states with a fixed linear momentum around the $S^1$ as the particles are given more and more boost momentum. At the critical point when the spacetime is about to develop closed timelike curves, the number of states again tends to zero. Thus it seems that quantum mechanics naturally enforces the chronology protection conjecture by superselecting the causality violating field configurations from the quantum mechanical phase space.Comment: 20 pages, Late

The roles of charge exchange and dissociation in spreading Saturn's neutral clouds

Neutrals sourced directly from Enceladus's plumes are initially confined to a dense neutral torus in Enceladus's orbit around Saturn. This neutral torus is redistributed by charge exchange, impact/photodissociation, and neutral-neutral collisions to produce Saturn's neutral clouds. Here we consider the former processes in greater detail than in previous studies. In the case of dissociation, models have assumed that OH is produced with a single speed of 1 km/s, whereas laboratory measurements suggest a range of speeds between 1 and 1.6 km/s. We show that the high-speed case increases dissociation's range of influence from 9 to 15 Rs. For charge exchange, we present a new modeling approach, where the ions are followed within a neutral background, whereas neutral cloud models are conventionally constructed from the neutrals' point of view. This approach allows us to comment on the significance of the ions' gyrophase at the moment charge exchange occurs. Accounting for gyrophase: (1) has no consequence on the H2O cloud; (2) doubles the local density of OH at the orbit of Enceladus; and (3) decreases the oxygen densities at Enceladus's orbit by less than 10%. Finally, we consider velocity-dependent, as well as species-dependent cross sections and find that the oxygen cloud produced from charge exchange is spread out more than H2O, whereas the OH cloud is the most confined.Comment: Accepted to the Journal of Geophysical Research, 49 pages, 10 figure

Lithium Intercalation into the Excitonic Insulator Candidate Ta2NiSe5

A new reduced phase derived from the excitonic insulator candidate Ta2NiSe5 has been synthesized via the intercalation of lithium. LiTa2NiSe5 crystallizes in the orthorhombic space group Pmnb (no. 62) with lattice parameters a = 3.50247(3) Å, b = 13.4053(4) Å, c = 15.7396(2) Å, and Z = 4, with an increase of the unit cell volume by 5.44(1)% compared with Ta2NiSe5. Significant rearrangement of the Ta-Ni-Se layers is observed, in particular a very significant relative displacement of the layers compared to the parent phase, similar to that which occurs under hydrostatic pressure. Neutron powder diffraction experiments and computational analysis confirm that Li occupies a distorted triangular prismatic site formed by Se atoms of adjacent Ta2NiSe5 layers with an average Li-Se bond length of 2.724(2) Å. Li-NMR experiments show a single Li environment at ambient temperature. Intercalation suppresses the distortion to monoclinic symmetry that occurs in Ta2NiSe5 at 328 K and that is believed to be driven by the formation of an excitonic insulating state. Magnetometry data show that the reduced phase has a smaller net diamagnetic susceptibility than Ta2NiSe5 due to the enhancement of the temperature-independent Pauli paramagnetism caused by the increased density of states at the Fermi level evident also from the calculations, consistent with the injection of electrons during intercalation and formation of a metallic phase

Statistical mixing and aggregation in Feller diffusion

We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate - a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales.Comment: 16 pages, 3 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen