Riesz transform characterization of Hardy spaces associated with Schr\"odinger operators with compactly supported potentials

Let L=-\Delta+V be a Schr\"odinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semigroup generated by -L. We say that an L^1(R^d)-function f belongs to the Hardy space H_L^1 associated with L if sup_{t>0} |K_t f| belongs to L^1(R^d). We prove that f\in H_L^1 if and only if R_j f \in L^1(R^d) for j=1,...,d, where R_j= \frac{d}{dx_j} L^{-1/2} are the Riesz transforms associated with L.Comment: 6 page

Laboratory evaluation of the effect of nitric acid uptake on frost point hygrometer performance

Chilled mirror hygrometers (CMH) are widely used to measure water vapour in the troposphere and lower stratosphere from balloon-borne sondes. Systematic discrepancies among in situ water vapour instruments have been observed at low water vapour mixing ratios (<5 ppm) in the upper troposphere and lower stratosphere (UT/LS). Understanding the source of the measurement discrepancies is important for a more accurate and reliable determination of water vapour abundance in this region. We have conducted a laboratory study to investigate the potential interference of gas-phase nitric acid (HNO<sub>3</sub>) with the measurement of frost point temperature, and consequently the water vapour mixing ratio, determined by CMH under conditions representative of operation in the UT/LS. No detectable interference in the measured frost point temperature was found for HNO<sub>3</sub> mixing ratios of up to 4 ppb for exposure times up to 150 min. HNO<sub>3</sub> was observed to co-condense on the mirror frost, with the adsorbed mass increasing linearly with time at constant exposure levels. Over the duration of a typical balloon sonde ascent (90–120 min), the maximum accumulated HNO<sub>3</sub> amounts were comparable to monolayer coverage of the geometric mirror surface area, which corresponds to only a small fraction of the actual frost layer surface area. This small amount of co-condensed HNO<sub>3</sub> is consistent with the observed lack of HNO<sub>3</sub> interference in the frost point measurement because the CMH utilizes significant reductions (>10%) in surface reflectivity by the condensate to determine H<sub>2</sub>O

Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions

The survival probability, S_N(t), of a diffusing prey (``lamb'') in the proximity of N diffusing predators (a ``pride of lions'') in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S_N(t) is proportional to t^{-beta_N}, with the decay exponent beta_N proportional to ln N. The crossover behavior as a function of the relative diffusivities of the lions and the lamb is also discussed. When N--->oo, the lamb survival probability exhibits a log-normal decay, exp(-ln^2 t).Comment: 12 pages, no figures, macro files prepended, to be submitted to J. Phys.

Bromine measurements in ozone depleted air over the Arctic Ocean

In situ measurements of ozone, photochemically active bromine compounds, and other trace gases over the Arctic Ocean in April 2008 are used to examine the chemistry and geographical extent of ozone depletion in the arctic marine boundary layer (MBL). Data were obtained from the NOAA WP-3D aircraft during the Aerosol, Radiation, and Cloud Processes affecting Arctic Climate (ARCPAC) study and the NASA DC-8 aircraft during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) study. Fast (1 s) and sensitive (detection limits at the low pptv level) measurements of BrCl and BrO were obtained from three different chemical ionization mass spectrometer (CIMS) instruments, and soluble bromide was measured with a mist chamber. The CIMS instruments also detected Br2. Subsequent laboratory studies showed that HOBr rapidly converts to Br2 on the Teflon instrument inlets. This detected Br2 is identified as active bromine and represents a lower limit of the sum HOBr + Br2. The measured active bromine is shown to likely be HOBr during daytime flights in the arctic. In the MBL over the Arctic Ocean, soluble bromide and active bromine were consistently elevated and ozone was depleted. Ozone depletion and active bromine enhancement were confined to the MBL that was capped by a temperature inversion at 200–500 m altitude. In ozone-depleted air, BrO rarely exceeded 10 pptv and was always substantially lower than soluble bromide that was as high as 40 pptv. BrCl was rarely enhanced above the 2 pptv detection limit, either in the MBL, over Alaska, or in the arctic free troposphere

Thermodynamics and Universality for Mean Field Quantum Spin Glasses

We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin glass models to answer analogous questions about quantum models.Comment: 17 page

Fine material in grain

Fine material in grain: an overview / Richard Stroshine -- Factors that affect the costs of fines in the corn export market / Lowell D. Hill, Mack Leath -- Effects of fine material on mold growth in grain / David B. Sauer, Richard A. Meronuck, John Tuite -- Effects of fine material on insect infestation: a review / Paul W. Flinn, William H. McGaughey, Wendell E. Burkholder -- Reducing or controlling damage to grain from handling: a review / Charles R. Martin, George H. Foster -- Evaluating grain for potential production of fine material - breakage susceptibility testing / Steven R. Eckhoff -- Genotypic differences in breakage susceptibility of corn and soybeans -- M. R. Paulsen, L. L. Darrah, R. L. Stroshin

Pollutant dispersion in a developing valley cold-air pool

Pollutants are trapped and accumulate within cold-air pools, thereby affecting air quality. A numerical model is used to quantify the role of cold-air-pooling processes in the dispersion of air pollution in a developing cold-air pool within an alpine valley under decoupled stable conditions. Results indicate that the negatively buoyant downslope flows transport and mix pollutants into the valley to depths that depend on the temperature deficit of the flow and the ambient temperature structure inside the valley. Along the slopes, pollutants are generally entrained above the cold-air pool and detrained within the cold-air pool, largely above the ground-based inversion layer. The ability of the cold-air pool to dilute pollutants is quantified. The analysis shows that the downslope flows fill the valley with air from above, which is then largely trapped within the cold-air pool, and that dilution depends on where the pollutants are emitted with respect to the positions of the top of the ground-based inversion layer and cold-air pool, and on the slope wind speeds. Over the lower part of the slopes, the cold-air-pool-averaged concentrations are proportional to the slope wind speeds where the pollutants are emitted, and diminish as the cold-air pool deepens. Pollutants emitted within the ground-based inversion layer are largely trapped there. Pollutants emitted farther up the slopes detrain within the cold-air pool above the ground-based inversion layer, although some fraction, increasing with distance from the top of the slopes, penetrates into the ground-based inversion layer.Peer reviewe

1,2-Dichlorohexafluoro-Cyclobutane (1,2-c-C4F6Cl2, R-316c) a Potent Ozone Depleting Substance and Greenhouse Gas: Atmospheric Loss Processes, Lifetimes, and Ozone Depletion and Global Warming Potentials for the (E) and (Z) stereoisomers

The atmospheric processing of (E)- and (Z)-1,2-dichlorohexafluorocyclobutane (1,2-c-C4F6Cl2, R-316c) was examined in this work as the ozone depleting (ODP) and global warming (GWP) potentials of this proposed replacement compound are presently unknown. The predominant atmospheric loss processes and infrared absorption spectra of the R-316c isomers were measured to provide a basis to evaluate their atmospheric lifetimes and, thus, ODPs and GWPs. UV absorption spectra were measured between 184.95 to 230 nm at temperatures between 214 and 296 K and a parametrization for use in atmospheric modeling is presented. The Cl atom quantum yield in the 193 nm photolysis of R- 316c was measured to be 1.90 +/- 0.27. Hexafluorocyclobutene (c-C4F6) was determined to be a photolysis co-product with molar yields of 0.7 and 1.0 (+/-10%) for (E)- and (Z)-R-316c, respectively. The 296 K total rate coefficient for the O(1D) + R-316c reaction, i.e., O(1D) loss, was measured to be (1.56 +/- 0.11) 10(exp 10)cu cm/ molecule/s and the reactive rate coefficient, i.e., R-316c loss, was measured to be (1.36 +/- 0.20) 10(exp 10)cu cm/molecule/s corresponding to a approx. 88% reactive yield. Rate coefficient upper-limits for the OH and O3 reaction with R-316c were determined to be <2.3 10(exp 17) and <2.0 10(exp 22)cu cm/molecule/s, respectively, at 296 K. The quoted uncertainty limits are 2(sigma) and include estimated systematic errors. Local and global annually averaged lifetimes for the (E)- and (Z)-R-316c isomers were calculated using a 2-D atmospheric model to be 74.6 +/- 3 and 114.1 +/-10 years, respectively, where the estimated uncertainties are due solely to the uncertainty in the UV absorption spectra. Stratospheric photolysis is the predominant atmospheric loss process for both isomers with the O(1D) reaction making a minor, approx. 2% for the (E) isomer and 7% for the (Z) isomer, contribution to the total atmospheric loss. Ozone depletion potentials for (E)- and (Z)-R-316c were calculated using the 2-D model to be 0.46 and 0.54, respectively. Infrared absorption spectra for (E)- and (Z)-R-316c were measured at 296 K and used to estimate their radiative efficiencies (REs) and GWPs; 100-year time-horizon GWPs of 4160 and 5400 were obtained for (E)- and (Z)-R-316c, respectively. Both isomers of R-316c are shown in this work to be long-lived ozone depleting substances and potent greenhouse gases