Finite size effects on measures of critical exponents in d=3 O(N) models

We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte Carlo values, but in agreement with $\epsilon$-expansions. We also measure the critical exponent related with the tensorial magnetization as well as the $\nu$ exponents and critical couplings.Comment: 12 pages, 2 postscript figure

Absence of Evidence Is Not Evidence of Absence: The Color-Density Relation at Fixed Stellar Mass Persists to z ~ 1

We use data drawn from the DEEP2 Galaxy Redshift Survey to investigate the relationship between local galaxy density, stellar mass, and rest-frame galaxy color. At z ~ 0.9, we find that the shape of the stellar mass function at the high-mass (log (M*/Msun) > 10.1) end depends on the local environment, with high-density regions favoring more massive systems. Accounting for this stellar mass-environment relation (i.e., working at fixed stellar mass), we find a significant color-density relation for galaxies with 10.6 < log(M*/Msun) < 11.1 and 0.75 < z < 0.95. This result is shown to be robust to variations in the sample selection and to extend to even lower masses (down to log(M*/Msun) ~ 10.4). We conclude by discussing our results in comparison to recent works in the literature, which report no significant correlation between galaxy properties and environment at fixed stellar mass for the same redshift and stellar mass domain. The non-detection of environmental dependence found in other data sets is largely attributable to their smaller samples size and lower sampling density, as well as systematic effects such as inaccurate redshifts and biased analysis techniques. Ultimately, our results based on DEEP2 data illustrate that the evolutionary state of a galaxy at z ~ 1 is not exclusively determined by the stellar mass of the galaxy. Instead, we show that local environment appears to play a distinct role in the transformation of galaxy properties at z > 1.Comment: 10 pages, 5 Figures; Accepted for publication in MNRA

The effect of surface character on flows in microchannels

A technique for quantifying velocity profiles of fluids flowing in circular microchannels is presented. The primary purpose of this technique is to provide a robust method for quantifying the effect Of Surface character on the bulk fluid behaviour. A laser-scanning confocal microscope has been used to obtain fluorescent particle images from a 1 micron thick plane along the centreline of hydrophobic and hydrophilic glass capillaries. The velocities of fluorescent particles being carried in pressure-driven laminar flow of a Newtonian fluid have been evaluated at the centreplane of 57.5 micron capillaries using a variation of particle tracking velocimetry (PTV). This work aims to clarify inconsistencies in previously reported [1-12] slip velocities observed in water over hydrophobically modified surfaces at micron and submicron lengthscales. A change in the velocity profile is observed for water flowing in hydrophobic capillaries, although the behaviour appears to be a result of an optical distortion at the fluid-wall interface. This may point to previous suggestions of a thin layer of air adsorbing to the surface. Notwithstanding, the results do not confidently suggest evidence of slip of water on hydrophobic surfaces in microchannels

Mapping of shape invariant potentials by the point canonical transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the P\"{o}schl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulth\'{e}n potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for P\"{o}schl-Teller type I and Hulth\'{e}n is SU(2)

The mean curvature at the first singular time of the mean curvature flow

Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. We prove that the mean curvature blows up at the first singular time $T$ if all singularities are of type I. In the case $n = 2$, regardless of the type of a possibly forming singularity, we show that at the first singular time the mean curvature necessarily blows up provided that either the Multiplicity One Conjecture holds or the Gaussian density is less than two. We also establish and give several applications of a local regularity theorem which is a parabolic analogue of Choi-Schoen estimate for minimal submanifolds

Differential effects of partial and complete loss of TREM2 on microglial injury response and tauopathy.

Alzheimer's disease (AD), the most common form of dementia, is characterized by the abnormal accumulation of amyloid plaques and hyperphosphorylated tau aggregates, as well as microgliosis. Hemizygous missense variants in Triggering Receptor Expressed on Myeloid Cells 2 (TREM2) are associated with elevated risk for developing late-onset AD. These variants are hypothesized to result in loss of function, mimicking TREM2 haploinsufficiency. However, the consequences of TREM2 haploinsufficiency on tau pathology and microglial function remain unknown. We report the effects of partial and complete loss of TREM2 on microglial function and tau-associated deficits. In vivo imaging revealed that microglia from aged TREM2-haploinsufficient mice show a greater impairment in their injury response compared with microglia from aged TREM2-KO mice. In transgenic mice expressing mutant human tau, TREM2 haploinsufficiency, but not complete loss of TREM2, increased tau pathology. In addition, whereas complete TREM2 deficiency protected against tau-mediated microglial activation and atrophy, TREM2 haploinsufficiency elevated expression of proinflammatory markers and exacerbated atrophy at a late stage of disease. The differential effects of partial and complete loss of TREM2 on microglial function and tau pathology provide important insights into the critical role of TREM2 in AD pathogenesis

The Evolution of Galaxy Mergers and Morphology at z<1.2 in the Extended Groth Strip

We present the quantitative rest-frame B morphological evolution and galaxy merger fractions at 0.2 < z < 1.2 as observed by the All-wavelength Extended Groth Strip International Survey (AEGIS). We use the Gini coefficent and M_20 to identify major mergers and classify galaxy morphology for a volume-limited sample of 3009 galaxies brighter than 0.4 L_B^*, assuming pure luminosity evolution of 1.3 M_B per unit redshift. We find that the merger fraction remains roughly constant at 10 +/- 2% for 0.2 < z < 1.2. The fraction of E/S0/Sa increases from 21+/- 3% at z ~ 1.1 to 44 +/- 9% at z ~ 0.3, while the fraction of Sb-Ir decreases from 64 +/- 6% at z ~ 1.1 to 47 +/- 9% at z ~ 0.3. The majority of z 10^11 L_sun are disk galaxies, and only ~ 15% are classified as major merger candidates. Edge-on and dusty disk galaxies (Sb-Ir) are almost a third of the red sequence at z ~ 1.1, while E/S0/Sa makeup over 90% of the red sequence at z ~ 0.3. Approximately 2% of our full sample are red mergers. We conclude (1) the galaxy merger rate does not evolve strongly between 0.2 < z < 1.2; (2) the decrease in the volume-averaged star-formation rate density since z ~ 1 is a result of declining star-formation in disk galaxies rather than a disappearing population of major mergers; (3) the build-up of the red sequence at z < 1 can be explained by a doubling in the number of spheroidal galaxies since z ~ 1.2.Comment: 24 pages, including 3 tables and 18 color figures; accepted to the Astrophysical Journal; high resolution version available at http://www.noao.edu/noao/staff/lotz/lotz_mergers.pd

Fire effects on aquatic ecosystems: an assessment of the current state of science

Fire is a prevalent feature of many landscapes and has numerous and complex effects on geological, hydrological, ecological, and economic systems. In some regions, the frequency and intensity of wildfire have increased in recent years and are projected to escalate with predicted climatic and landuse changes. In addition, prescribed burns continue to be used in many parts of the world to clear vegetation for development projects, encourage desired vegetation, and reduce fuel loads. Given the prevalence of fire on the landscape, authors of papers in this special series examine the complexities of fire as a disturbance shaping freshwater ecosystems and highlight the state of the science. These papers cover key aspects of fire effects that range from vegetation loss and recovery in watersheds to effects on hydrology and water quality with consequences for communities (from algae to fish), food webs, and ecosystem processes (e.g., organic matter subsidies, nutrient cycling) across a range of scales. The results presented in this special series of articles expand our knowledge of fire effects in different biomes, water bodies, and geographic regions, encompassing aquatic population, community, and ecosystem responses. In this overview, we summarize each paper and emphasize its contributions to knowledge on fire ecology and freshwater ecosystems. This overview concludes with a list of 7 research foci that are needed to further our knowledge of fire effects on aquatic ecosystems, including research on: 1) additional biomes and geographic regions; 2) additional habitats, including wetlands and lacustrine ecosystems; 3) different fire severities, sizes, and spatial configurations; and 4) additional response variables (e.g., ecosystem processes) 5) over long (>5 y) time scales 6) with more rigorous study designs and data analyses, and 7) consideration of the effects of fire management practices and policies on aquatic ecosystems