Invariants for E_0-semigroups on II_1 factors

We introduce four new cocycle conjugacy invariants for E_0-semigroups on II_1 factors: a coupling index, a dimension for the gauge group, a super product system and a C*-semiflow. Using noncommutative It\^o integrals we show that the dimension of the gauge group can be computed from the structure of the additive cocycles. We do this for the Clifford flows and even Clifford flows on the hyperfinite II_1 factor, and for the free flows on the free group factor $L(F_\infty)$. In all cases the index is 0, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the C*-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate E_0-semigroups.Comment: 51 page

Inborn Errors of Metabolism in the Era of Untargeted Metabolomics and Lipidomics.

Inborn errors of metabolism (IEMs) are a group of inherited diseases with variable incidences. IEMs are caused by disrupting enzyme activities in specific metabolic pathways by genetic mutations, either directly or indirectly by cofactor deficiencies, causing altered levels of compounds associated with these pathways. While IEMs may present with multiple overlapping symptoms and metabolites, early and accurate diagnosis of IEMs is critical for the long-term health of affected subjects. The prevalence of IEMs differs between countries, likely because different IEM classifications and IEM screening methods are used. Currently, newborn screening programs exclusively use targeted metabolic assays that focus on limited panels of compounds for selected IEM diseases. Such targeted approaches face the problem of false negative and false positive diagnoses that could be overcome if metabolic screening adopted analyses of a broader range of analytes. Hence, we here review the prospects of using untargeted metabolomics for IEM screening. Untargeted metabolomics and lipidomics do not rely on predefined target lists and can detect as many metabolites as possible in a sample, allowing to screen for many metabolic pathways simultaneously. Examples are given for nontargeted analyses of IEMs, and prospects and limitations of different metabolomics methods are discussed. We conclude that dedicated studies are needed to compare accuracy and robustness of targeted and untargeted methods with respect to widening the scope of IEM diagnostics

Droplet impact on a thin fluid layer

The initial stages of high-velocity droplet impact on a shallow water layer are described, with special emphasis given to the spray jet mechanics. Four stages of impact are delineated, with appropriate scalings, and the successively more important influence of the base is analysed. In particular, there is a finite time before which part of the water in the layer remains under the droplet and after which all of the layer is ejected in the splash jet

Magnetic Fields in Dark Cloud Cores: Arecibo OH Zeeman Observations

We have carried out an extensive survey of magnetic field strengths toward dark cloud cores in order to test models of star formation: ambipolar-diffusion driven or turbulence driven. The survey involved $\sim500$ hours of observing with the Arecibo telescope in order to make sensitive OH Zeeman observations toward 34 dark cloud cores. Nine new probable detections were achieved at the 2.5-sigma level; the certainty of the detections varies from solid to marginal, so we discuss each probable detection separately. However, our analysis includes all the measurements and does not depend on whether each position has a detection or just a sensitive measurement. Rather, the analysis establishes mean (or median) values over the set of observed cores for relevant astrophysical quantities. The results are that the mass-to-flux ratio is supercritical by $\sim 2$, and that the ratio of turbulent to magnetic energies is also $\sim 2$. These results are compatible with both models of star formation. However, these OH Zeeman observations do establish for the first time on a statistically sound basis the energetic importance of magnetic fields in dark cloud cores at densities of order $10^{3-4}$ cm$^{-3}$, and they lay the foundation for further observations that could provide a more definitive test.Comment: 22 pages, 2 figures, 2 table

Long-term variation in the Sun's activity caused by magnetic Rossby waves in the tachocline

Long-term records of sunspot number and concentrations of cosmogenic radionuclides (10Be and 14C) on the Earth reveal the variation of the Sun's magnetic activity over hundreds and thousands of years. We identify several clear periods in sunspot, 10Be, and 14C data as 1000, 500, 350, 200 and 100 years. We found that the periods of the first five spherical harmonics of the slow magnetic Rossby mode in the presence of a steady toroidal magnetic field of 1200-1300 G in the lower tachocline are in perfect agreement with the time scales of observed variations. The steady toroidal magnetic field can be generated in the lower tachocline either due to the steady dynamo magnetic field for low magnetic diffusivity or due to the action of the latitudinal differential rotation on the weak poloidal primordial magnetic field, which penetrates from the radiative interior. The slow magnetic Rossby waves lead to variations of the steady toroidal magnetic field in the lower tachocline, which modulate the dynamo magnetic field and consequently the solar cycle strength. This result constitutes a key point for long-term prediction of the cycle strength. According to our model, the next deep minimum in solar activity is expected during the first half of this century.Comment: 4 pages, 4 figures, accepted in ApJ

Photophoretic Structuring of Circumstellar Dust Disks

We study dust accumulation by photophoresis in optically thin gas disks. Using formulae of the photophoretic force that are applicable for the free molecular regime and for the slip-flow regime, we calculate dust accumulation distances as a function of the particle size. It is found that photophoresis pushes particles (smaller than 10 cm) outward. For a Sun-like star, these particles are transported to 0.1-100 AU, depending on the particle size, and forms an inner disk. Radiation pressure pushes out small particles (< 1 mm) further and forms an extended outer disk. Consequently, an inner hole opens inside ~0.1 AU. The radius of the inner hole is determined by the condition that the mean free path of the gas molecules equals the maximum size of the particles that photophoresis effectively works on (100 micron - 10 cm, depending on the dust property). The dust disk structure formed by photophoresis can be distinguished from the structure of gas-free dust disk models, because the particle sizes of the outer disks are larger, and the inner hole radius depends on the gas density.Comment: 15 pages, 9 figures, Accepted by ApJ; corrected a typo in the author nam