Ramanujan sums for signal processing of low frequency noise

An aperiodic (low frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as M\"obius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low frequency regime. In place we introduce a new signal processing tool based on the Ramanujan sums c_q(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasi-periodic versus the time n of the resonance and aperiodic versus the order q of the resonance. New results arise from the use of this Ramanujan-Fourier transform (RFT) in the context of arithmetical and experimental signalsComment: 11 pages in IOP style, 14 figures, 2 tables, 16 reference

Spectral line shape of resonant four-wave mixing induced by broad-bandwidth lasers

We present a theoretical and experimental study of the line shape of resonant four-wave mixing induced by broad-bandwidth laser radiation that revises the theory of Meacher, Smith, Ewart, and Cooper (MSEC) [Phys. Rev. A 46, 2718 (1992)]. We adopt the same method as MSEC but correct for an invalid integral used to average over the distribution of atomic velocities. The revised theory predicts a Voigt line shape composed of a homogeneous, Lorentzian component, defined by the collisional rate Γ, and an inhomogeneous, Doppler component, which is a squared Gaussian. The width of the inhomogeneous component is reduced by a factor of √2 compared to the simple Doppler width predicted by MSEC. In the limit of dominant Doppler broadening, the width of the homogeneous component is predicted to be 4Γ, whereas in the limit of dominant homogeneous broadening, the predicted width is 2Γ. An experimental measurement is reported of the line shape of the four-wave-mixing signal using a broad-bandwidth, "modeless", laser resonant with the Q1 (6) line of the A2 Σ - X2 Π(0,0) system of the hydroxyl radical. The measured widths of the Voigt components were found to be consistent with the predictions of the revised theory

L2 series solutions of the Dirac equation for power-law potentials at rest mass energy

We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are written in terms of the confluent hypergeometric function and chosen such that the matrix representation of the Dirac operator is tridiagonal. The "wave equation" results in a three-term recursion relation for the expansion coefficients of the spinor wavefunction which is solved in terms of orthogonal polynomials. These are modified versions of the Meixner-Pollaczek polynomials and of the continuous dual Hahn polynomials. The choice depends on the values of the angular momentum and the power of the potential.Comment: 13 pages, 1 Tabl

Detailed investigation of the superconducting transition of niobium disks exhibiting the paramagnetic Meissner effect

The superconducting transition region in a Nb disk showing the paramagnetic Meissner effect (PME) has been investigated in detail. From the field-cooled magnetization behavior, two well-defined temperatures can be associated with the appearance of the PME: T_1 (< T_c) indicates the characteristic temperature where the paramagnetic moment first appears and a lower temperature T_p (< T_1) defines the temperature where the positive moment no longer increases. During the subsequent warming, the paramagnetic moment begins to decrease at T_p and then vanishes at T_1 with the magnitude of the magnetization change between these two temperatures being nearly the same as that during cooling. This indicates that the nature of the PME is reversible and not associated with flux motion. Furthermore, the appearance of this paramagnetic moment is even observable in fields as large as 0.2 T even though the magnetization does not remain positive to the lowest temperatures. Magnetic hysteresis loops in the temperature range between T_1 and T_p also exhibit a distinct shape that is different from the archetypal shape of a bulk type-II superconductor. These behaviors are discussed in terms of the so-called 'giant vortex state'.Comment: Total 4 printed pages, 4 Figure

Dual-Pump Coherent Anti-Stokes Raman Scattering Temperature and CO2 Concentration Measurements

Measurements of temperature and CO2 concentration using dual-pump coherent anti-Stokes Raman scattering, (CARS) are described. The measurements were performed in laboratory flames,in a room-temperature gas cell, and on an engine test stand at the U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base. A modeless dye laser, a single-mode Nd:YAG laser, and an unintensified back-illuminated charge-coupled device digital camera were used for these measurements. The CARS measurements were performed on a single-laser-shot basis. The standard deviations of the temperatures and CO2 mole fractions determined from single-shot dual-pump CARS spectra in steady laminar propane/air flames were approximately 2 and 10% of the mean values of approximately 2000 K and 0.10, respectively. The precision and accuracy of single-shot temperature measurements obtained from the nitrogen part of the dual-pump CARS system were investigated in detail in near-adiabatic hydrogen/air/CO2 flames. The precision of the CARS temperature measurements was found to be comparable to the best results reported in the literature for conventional two-laser, single-pump CARS. The application of dual-pump CARS for single-shot measurements in a swirl-stabilized combustor fueled with JP-8 was also demonstrated

Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations

SO(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb and Morse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the oscillator potential by point canonical transformations. We call this class the "oscillator class". A nontrivial graded extension of SO(2,1) is defined and its realization by two-dimensional matrices of differential operators acting in spinor space is given. It turns out that this graded algebra is the supersymmetry algebra for a class of relativistic potentials that includes the Dirac-Oscillator, Dirac-Coulomb and Dirac-Morse potentials. This class is, in fact, the relativistic extension of the oscillator class. A new point canonical transformation, which is compatible with the relativistic problem, is formulated. It maps all of these relativistic potentials into the Dirac-Oscillator potential.Comment: Replaced with a more potrable PDF versio

Impacts of large-scale climatic disturbances on the terrestrial carbon cycle

BACKGROUND: The amount of carbon dioxide in the atmosphere steadily increases as a consequence of anthropogenic emissions but with large interannual variability caused by the terrestrial biosphere. These variations in the CO(2 )growth rate are caused by large-scale climate anomalies but the relative contributions of vegetation growth and soil decomposition is uncertain. We use a biogeochemical model of the terrestrial biosphere to differentiate the effects of temperature and precipitation on net primary production (NPP) and heterotrophic respiration (Rh) during the two largest anomalies in atmospheric CO(2 )increase during the last 25 years. One of these, the smallest atmospheric year-to-year increase (largest land carbon uptake) in that period, was caused by global cooling in 1992/93 after the Pinatubo volcanic eruption. The other, the largest atmospheric increase on record (largest land carbon release), was caused by the strong El Niño event of 1997/98. RESULTS: We find that the LPJ model correctly simulates the magnitude of terrestrial modulation of atmospheric carbon anomalies for these two extreme disturbances. The response of soil respiration to changes in temperature and precipitation explains most of the modelled anomalous CO(2 )flux. CONCLUSION: Observed and modelled NEE anomalies are in good agreement, therefore we suggest that the temporal variability of heterotrophic respiration produced by our model is reasonably realistic. We therefore conclude that during the last 25 years the two largest disturbances of the global carbon cycle were strongly controlled by soil processes rather then the response of vegetation to these large-scale climatic events

Circulating adrenomedullin estimates survival and reversibility of organ failure in sepsis: the prospective observational multinational Adrenomedullin and Outcome in Sepsis and Septic Shock-1 (AdrenOSS-1) study

Background: Adrenomedullin (ADM) regulates vascular tone and endothelial permeability during sepsis. Levels of circulating biologically active ADM (bio-ADM) show an inverse relationship with blood pressure and a direct relationship with vasopressor requirement. In the present prospective observational multinational Adrenomedullin and Outcome in Sepsis and Septic Shock 1 (, AdrenOSS-1) study, we assessed relationships between circulating bio-ADM during the initial intensive care unit (ICU) stay and short-term outcome in order to eventually design a biomarker-guided randomized controlled trial. Methods: AdrenOSS-1 was a prospective observational multinational study. The primary outcome was 28-day mortality. Secondary outcomes included organ failure as defined by Sequential Organ Failure Assessment (SOFA) score, organ support with focus on vasopressor/inotropic use, and need for renal replacement therapy. AdrenOSS-1 included 583 patients admitted to the ICU with sepsis or septic shock. Results: Circulating bio-ADM levels were measured upon admission and at day 2. Median bio-ADM concentration upon admission was 80.5 pg/ml [IQR 41.5-148.1 pg/ml]. Initial SOFA score was 7 [IQR 5-10], and 28-day mortality was 22%. We found marked associations between bio-ADM upon admission and 28-day mortality (unadjusted standardized HR 2.3 [CI 1.9-2.9]; adjusted HR 1.6 [CI 1.1-2.5]) and between bio-ADM levels and SOFA score (p &lt; 0.0001). Need of vasopressor/inotrope, renal replacement therapy, and positive fluid balance were more prevalent in patients with a bio-ADM &gt; 70 pg/ml upon admission than in those with bio-ADM ≤ 70 pg/ml. In patients with bio-ADM &gt; 70 pg/ml upon admission, decrease in bio-ADM below 70 pg/ml at day 2 was associated with recovery of organ function at day 7 and better 28-day outcome (9.5% mortality). By contrast, persistently elevated bio-ADM at day 2 was associated with prolonged organ dysfunction and high 28-day mortality (38.1% mortality, HR 4.9, 95% CI 2.5-9.8). Conclusions: AdrenOSS-1 shows that early levels and rapid changes in bio-ADM estimate short-term outcome in sepsis and septic shock. These data are the backbone of the design of the biomarker-guided AdrenOSS-2 trial. Trial registration: ClinicalTrials.gov, NCT02393781. Registered on March 19, 2015

Indication for the disappearance of reactor electron antineutrinos in the Double Chooz experiment

The Double Chooz Experiment presents an indication of reactor electron antineutrino disappearance consistent with neutrino oscillations. A ratio of 0.944 $\pm$ 0.016 (stat) $\pm$ 0.040 (syst) observed to predicted events was obtained in 101 days of running at the Chooz Nuclear Power Plant in France, with two 4.25 GW$_{th}$ reactors. The results were obtained from a single 10 m$^3$ fiducial volume detector located 1050 m from the two reactor cores. The reactor antineutrino flux prediction used the Bugey4 measurement as an anchor point. The deficit can be interpreted as an indication of a non-zero value of the still unmeasured neutrino mixing parameter \sang. Analyzing both the rate of the prompt positrons and their energy spectrum we find \sang = 0.086 $\pm$ 0.041 (stat) $\pm$ 0.030 (syst), or, at 90% CL, 0.015 $<$ \sang $\ <$ 0.16.Comment: 7 pages, 4 figures, (new version after PRL referee's comments

Effect of smoke on subcanopy shaded light, canopy temperature, and carbon dioxide uptake in an Amazon rainforest

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95278/1/gbc1694.pd