Non-Lipschitz points and the SBV regularity of the minimum time function

This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$. We consider first the case of normal linear control systems with constant coefficients in $\mathbb{R}^N$. We characterize points around which $T$ is not Lipschitz as those which can be reached from the origin by an optimal trajectory (of the reversed dynamics) with vanishing minimized Hamiltonian. Linearity permits an explicit representation of such set, that we call $\mathcal{S}$. Furthermore, we show that $\mathcal{S}$ is $\mathcal{H}^{N-1}$-rectifiable with positive $\mathcal{H}^{N-1}$-measure. Second, we consider a class of control-affine \textit{planar} nonlinear systems satisfying a second order controllability condition: we characterize the set $\mathcal{S}$ in a neighborhood of the origin in a similar way and prove the $\mathcal{H}^1$-rectifiability of $\mathcal{S}$ and that $\mathcal{H}^1(\mathcal{S})>0$. In both cases, $T$ is known to have epigraph with positive reach, hence to be a locally $BV$ function (see \cite{CMW,GK}). Since the Cantor part of $DT$ must be concentrated in $\mathcal{S}$, our analysis yields that $T$ is $SBV$, i.e., the Cantor part of $DT$ vanishes. Our results imply also that $T$ is locally of class $\mathcal{C}^{1,1}$ outside a $\mathcal{H}^{N-1}$-rectifiable set. With small changes, our results are valid also in the case of multiple control input.Comment: 23 page

Microbial ecology of Thiobacillus ferrooxidans

FINAL TECHNICAL REPORT TO U.S. DEPARTMENT OF THE INTERIOR Geological Survey Washington. D.C.The contents of this report were developed in part under a grant from the Department of the Interior, U.S. Geological Survey. Grant number 14-08-0001-61313

Magneto-transport properties of monolayer borophene in perpendicular magnetic field: influence of electron-phonon interaction

The magneto-transport properties of a borophene monolayer in a perpendicular magnetic field B are studied via calculating the conductivity tensor and resistance under electron-optical phonon interaction by using the linear response theory. Numerical results are obtained and discussed for some specific parameters. The magnetic field-dependent longitudinal conductivity shows the magneto-phonon resonance effect that describes the transition of electrons between Landau levels by absorbing/emitting an optical phonon. The Hall conductivity increases first and then decreases with the magnetic field strength. Also, the longitudinal resistance increases significantly with increasing temperature, which shows the metal behaviour of the material. Practically, the observed magneto-phonon resonance can be applied to experimentally determine some material parameters, such as the distance between Landau levels and the optical phonon energy

Giant Spin Seebeck Effect through an Interface Organic Semiconductor

Interfacing an organic semiconductor C60 with a non-magnetic metallic thin film (Cu or Pt) has created a novel heterostructure that is ferromagnetic at ambient temperature, while its interface with a magnetic metal (Fe or Co) can tune the anisotropic magnetic surface property of the material. Here, we demonstrate that sandwiching C60 in between a magnetic insulator (Y3Fe5O12: YIG) and a non-magnetic, strong spin-orbit metal (Pt) promotes highly efficient spin current transport via the thermally driven spin Seebeck effect (SSE). Experiments and first principles calculations consistently show that the presence of C60 reduces significantly the conductivity mismatch between YIG and Pt and the surface perpendicular magnetic anisotropy of YIG, giving rise to enhanced spin mixing conductance across YIG/C60/Pt interfaces. As a result, a 600% increase in the SSE voltage (VLSSE) has been realized in YIG/C60/Pt relative to YIG/Pt. Temperature-dependent SSE voltage measurements on YIG/C60/Pt with varying C60 layer thicknesses also show an exponential increase in VLSSE at low temperatures below 200 K, resembling the temperature evolution of spin diffusion length of C60. Our study emphasizes the important roles of the magnetic anisotropy and the spin diffusion length of the intermediate layer in the SSE in YIG/C60/Pt structures, providing a new pathway for developing novel spin-caloric materials

Required flows for aquatic ecosystems in Ma River, Vietnam

Ecological flow requirements for the Ma River in dry season were assessed in three reaches of Ma – Buoi, Ma – Len and Ma – Chu. 5 indictor fish species was chosen based on biodiversity survey and roles of those species in aquatic ecosystem as well as local communities. Biological and hydrological data (dry season of 2016- 2017) and 35 year recorded hydrological data were collected and analyzed as input data for a physical habitat model River HYdraulic and HABitat SImulation Model – RHYHABSIM. Model results shown that the optimal flows of the reaches were very much higher compare with the minimum annual low flow - MALF. In this study, MALF7day were applied to calculate the recommended minimum flows of the three reaches. The recommended required minimum flows for Ma – Buoi, Ma – Len and Ma – Chu reaches were 51 m3/s, 49 m3/s and 61 m3/s, respectively. It must be stressed that this study only assessed whether or not there is enough habitat available for the river to sustain a healthy ecosystem

Large scale IRAM 30m CO-observations in the giant molecular cloud complex W43

We aim to give a full description of the distribution and location of dense molecular clouds in the giant molecular cloud complex W43. It has previously been identified as one of the most massive star-forming regions in our Galaxy. To trace the moderately dense molecular clouds in the W43 region, we initiated an IRAM 30m large program, named W43-HERO, covering a large dynamic range of scales (from 0.3 to 140 pc). We obtained on-the-fly-maps in 13CO (2-1) and C18O (2-1) with a high spectral resolution of 0.1 km/s and a spatial resolution of 12". These maps cover an area of ~1.5 square degrees and include the two main clouds of W43, as well as the lower density gas surrounding them. A comparison with Galactic models and previous distance calculations confirms the location of W43 near the tangential point of the Scutum arm at a distance from the Sun of approximately 6 kpc. The resulting intensity cubes of the observed region are separated into sub-cubes, centered on single clouds which are then analyzed in detail. The optical depth, excitation temperature, and H2 column density maps are derived out of the 13CO and C18O data. These results are then compared with those derived from Herschel dust maps. The mass of a typical cloud is several 10^4 solar masses while the total mass in the dense molecular gas (>100 cm^-3) in W43 is found to be about 1.9e6 solar masses. Probability distribution functions obtained from column density maps derived from molecular line data and Herschel imaging show a log-normal distribution for low column densities and a power-law tail for high densities. A flatter slope for the molecular line data PDF may imply that those selectively show the gravitationally collapsing gas

Strained Silicon Complementary TFET SRAM: Experimental Demonstration and Simulations

A half SRAM cell with strained Si nanowire complementary tunnel-FETs (TFETs) was fabricated and characterized to explore the feasibility and functionality of 6T-SRAM based on TFETs. Outward-faced n-TFETs are used as access-transistors. Static measurements were performed to determine the SRAM butterfly curves, allowing the assessment of cell functionality and stability. The forward p-i-n leakage of the access-transistor at certain bias configurations leads to malfunctioning storage operation, even without the contribution of the ambipolar behavior. At large VDD, lowering of the bit-line bias is needed to mitigate such effect, demonstrating functional hold, read and write operations. Circuit simulations were carried out using a Verilog-A compact model calibrated on the experimental TFETs, providing a better understanding of the TFET SRAM operation at different supply voltages and for different cell sizing and giving an estimate of the dynamic performance of the cell

Transaminase abnormalities and adaptations of the liver lobule manifest at specific cut-offs of steatosis

There is little documented evidence suggesting that liver fat is responsible for liver injury in the absence of other disease processes. We investigated the relationships between liver fat, aminotransferases and hepatic architecture in liver biopsies with simple steatosis. We identified 136 biopsies with simple steatosis from the Royal Free Hospital Archives with both clinical data and sufficient material. Digital image analysis was employed to measure fat proportionate area (mFPA). Hepatocyte area (HA) and lobule radius (LR) were also measured. There were significant increases in ALT (p < 0.001) and AST (p = 0.013) with increased fat content and evidence to suggest both 5% and 20% mFPA as a cut-off for raised ALT. In liver with increased fat content there were significant increases in HA (p < 0.001). LR also increased as mFPA increased to 10% (p < 0.001), at which point the lobule ceased to expand further and was counterbalanced with a decrease in the number of hepatocytes per lobule (p = 0.029). Consequently there are mechanisms of adaption in the liver architecture to accommodate the accumulation of fat and these are accompanied by significant increases in transaminases. These results support the generally accepted cut-off of 5% fat for steatosis and indicate 20% as a threshold of more severe liver injury

Environmental contamination with clostridioides (Clostridium) difficile in Vietnam

AIMS: To investigate the prevalence, molecular type, and antimicrobial susceptibility of Clostridioides difficile in the environment in Vietnam, where little is known about C. difficile. METHODS AND RESULTS: Samples of pig faeces, soils from pig farms, potatoes, and the hospital environment were cultured for C. difficile. Isolates were identified and typed by polymerase chain reaction (PCR) ribotyping. The overall prevalence of C. difficile contamination was 24.5% (68/278). Clostridioides difficile was detected mainly in soils from pig farms and hospital soils, with 70%-100% prevalence. Clostridioides difficile was isolated from 3.4% of pig faecal samples and 5% of potato surfaces. The four most prevalent ribotypes (RTs) were RTs 001, 009, 038, and QX574. All isolates were susceptible to metronidazole, fidaxomicin, vancomycin, and amoxicillin/clavulanate, while resistance to erythromycin, tetracycline, and moxifloxacin was common in toxigenic strains. Clostridioides difficile RTs 001A+B+CDT- and 038A-B-CDT- were predominantly multidrug resistant. CONCLUSIONS: Environmental sources of C. difficile are important to consider in the epidemiology of C. difficile infection in Vietnam, however, contaminated soils are likely to be the most important source of C. difficile. This poses additional challenges to controlling infections in healthcare settings