Diffusion-limited reactions and mortal random walkers in confined geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.Comment: 18 pages, 16 figure

Number of distinct sites visited by N random walkers on a Euclidean lattice

The evaluation of the average number S_N(t) of distinct sites visited up to time t by N independent random walkers all starting from the same origin on an Euclidean lattice is addressed. We find that, for the nontrivial time regime and for large N, S_N(t) \approx \hat S_N(t) (1-\Delta), where \hat S_N(t) is the volume of a hypersphere of radius (4Dt \ln N)^{1/2}, \Delta={1/2}\sum_{n=1}^\infty \ln^{-n} N \sum_{m=0}^n s_m^{(n)} \ln^{m} \ln N, d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the dimension and time. The first three terms of these series are calculated explicitly and the resulting expressions are compared with other approximations and with simulation results for dimensions 1, 2, and 3. Some implications of these results on the geometry of the set of visited sites are discussed.Comment: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev.

Haloperidol and Ziprasidone for Treatment of Delirium in Critical Illness

BACKGROUND: There are conflicting data on the effects of antipsychotic medications on delirium in patients in the intensive care unit (ICU). METHODS: In a randomized, double-blind, placebo-controlled trial, we assigned patients with acute respiratory failure or shock and hypoactive or hyperactive delirium to receive intravenous boluses of haloperidol (maximum dose, 20 mg daily), ziprasidone (maximum dose, 40 mg daily), or placebo. The volume and dose of a trial drug or placebo was halved or doubled at 12-hour intervals on the basis of the presence or absence of delirium, as detected with the use of the Confusion Assessment Method for the ICU, and of side effects of the intervention. The primary end point was the number of days alive without delirium or coma during the 14-day intervention period. Secondary end points included 30-day and 90-day survival, time to freedom from mechanical ventilation, and time to ICU and hospital discharge. Safety end points included extrapyramidal symptoms and excessive sedation. RESULTS: Written informed consent was obtained from 1183 patients or their authorized representatives. Delirium developed in 566 patients (48%), of whom 89% had hypoactive delirium and 11% had hyperactive delirium. Of the 566 patients, 184 were randomly assigned to receive placebo, 192 to receive haloperidol, and 190 to receive ziprasidone. The median duration of exposure to a trial drug or placebo was 4 days (interquartile range, 3 to 7). The median number of days alive without delirium or coma was 8.5 (95% confidence interval [CI], 5.6 to 9.9) in the placebo group, 7.9 (95% CI, 4.4 to 9.6) in the haloperidol group, and 8.7 (95% CI, 5.9 to 10.0) in the ziprasidone group (P=0.26 for overall effect across trial groups). The use of haloperidol or ziprasidone, as compared with placebo, had no significant effect on the primary end point (odds ratios, 0.88 [95% CI, 0.64 to 1.21] and 1.04 [95% CI, 0.73 to 1.48], respectively). There were no significant between-group differences with respect to the secondary end points or the frequency of extrapyramidal symptoms. CONCLUSIONS: The use of haloperidol or ziprasidone, as compared with placebo, in patients with acute respiratory failure or shock and hypoactive or hyperactive delirium in the ICU did not significantly alter the duration of delirium. (Funded by the National Institutes of Health and the VA Geriatric Research Education and Clinical Center; MIND-USA ClinicalTrials.gov number, NCT01211522 .)

A Lattice Study of the Magnetic Moment and the Spin Structure of the Nucleon

Using an approach free from momentum extrapolation, we calculate the nucleon magnetic moment and the fraction of the nucleon spin carried by the quark angular momentum in the quenched lattice QCD approximation. Quarks with three values of lattice masses, 210, 124 and 80 MeV, are formulated on the lattice using the standard Wilson approach. At every mass, 100 gluon configurations on 16^3 x 32 lattice with \beta=6.0 are used for statistical averaging. The results are compared with the previous calculations with momentum extrapolation. The contribution of the disconnected diagrams is studied at the largest quark mass using noise theory technique.Comment: 14 pages, 3 figures, Talk given at Lattice2001, Berlin, German

Highly Damped Quasinormal Modes of Kerr Black Holes: A Complete Numerical Investigation

We compute for the first time very highly damped quasinormal modes of the (rotating) Kerr black hole. Our numerical technique is based on a decoupling of the radial and angular equations, performed using a large-frequency expansion for the angular separation constant_{s}A_{l m}. This allows us to go much further in overtone number than ever before. We find that the real part of the quasinormal frequencies approaches a non-zero constant value which does not depend on the spin s of the perturbing field and on the angular index l: \omega_R=m\varpi(a). We numerically compute \varpi(a). Leading-order corrections to the asymptotic frequency are likely to be of order 1/\omega_I. The imaginary part grows without bound, the spacing between consecutive modes being a monotonic function of a.Comment: 5 pages, 3 figure

Precision Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetries A2

We have measured the spin structure functions g2p and g2d and the virtual photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 0.7 < Q^2 < 20 GeV^2 by scattering 29.1 and 32.3 GeV longitudinally polarized electrons from transversely polarized NH3 and 6LiD targets. Our measured g2 approximately follows the twist-2 Wandzura-Wilczek calculation. The twist-3 reduced matrix elements d2p and d2n are less than two standard deviations from zero. The data are inconsistent with the Burkhardt-Cottingham sum rule if there is no pathological behavior as x->0. The Efremov-Leader-Teryaev integral is consistent with zero within our measured kinematic range. The absolute value of A2 is significantly smaller than the sqrt[R(1+A1)/2] limit.Comment: 12 pages, 4 figures, 2 table

Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetry A2

We have measured the spin structure functions g2p and g2d and the virtual photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 1.0 < Q^2 < 30(GeV/c)^2 by scattering 38.8 GeV longitudinally polarized electrons from transversely polarized NH3 and 6LiD targets.The absolute value of A2 is significantly smaller than the sqrt{R} positivity limit over the measured range, while g2 is consistent with the twist-2 Wandzura-Wilczek calculation. We obtain results for the twist-3 reduced matrix elements d2p, d2d and d2n. The Burkhardt-Cottingham sum rule integral - int(g2(x)dx) is reported for the range 0.02 < x < 0.8.Comment: 12 pages, 4 figures, 1 tabl

Measurements of the Q2Q^2-Dependence of the Proton and Neutron Spin Structure Functions g1p and g1n

The structure functions g1p and g1n have been measured over the range 0.014 < x < 0.9 and 1 < Q2 < 40 GeV2 using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons. We find that the Q2 dependence of g1p (g1n) at fixed x is very similar to that of the spin-averaged structure function F1p (F1n). From a NLO QCD fit to all available data we find $\Gamma_1^p - \Gamma_1^n =0.176 \pm 0.003 \pm 0.007$ at Q2=5 GeV2, in agreement with the Bjorken sum rule prediction of 0.182 \pm 0.005.Comment: 17 pages, 3 figures. Submitted to Physics Letters

Mapping alveolar oxygen partial pressure in COPD using hyperpolarized helium-3: the multi-ethnic study of atherosclerosis (MESA) COPD study

Chronic obstructive pulmonary disease (COPD) and emphysema are characterized by functional and structural damage which increases the spaces for gaseous diffusion and impairs oxygen exchange. Here we explore the potential for hyperpolarized (HP) 3He MRI to characterize lung structure and function in a large-scale population-based study. Participants (n = 54) from the Multi-Ethnic Study of Atherosclerosis (MESA) COPD Study, a nested case-control study of COPD among participants with 10+ packyears underwent HP 3He MRI measuring pAO2, apparent diffusion coefficient (ADC), and ventilation. HP MRI measures were compared to full-lung CT and pulmonary function testing. High ADC values (>0.4 cm2/s) correlated with emphysema and heterogeneity in pAO2 measurements. Strong correlations were found between the heterogeneity of global pAO2 as summarized by its standard deviation (SD) (p < 0.0002) and non-physiologic pAO2 values (p < 0.0001) with percent emphysema on CT. A regional study revealed a strong association between pAO2 SD and visual emphysema severity (p < 0.003) and an association with the paraseptal emphysema subtype (p < 0.04) after adjustment for demographics and smoking status. HP noble gas pAO2 heterogeneity and the fraction of non-physiological pAO2 results increase in mild to moderate COPD. Measurements of pAO2 are sensitive to regional emphysematous damage detected by CT and may be used to probe pulmonary emphysema subtypes. HP noble gas lung MRI provides non-invasive information about COPD severity and lung function without ionizing radiation