Nested recursions with ceiling function solutions

Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \sum_{i=1}^k R(n-s_i-\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0, ..., R(c)=xi_c > 0, where the parameters are integers satisfying k > 0, p_i > 0 and a_ij > 0. We develop an algorithm to answer the following question: for an arbitrary rational number r/q, is there any set of values for k, p_i, s_i, a_ij and nu such that the ceiling function ceiling{rn/q} is the unique solution generated by R(n) with appropriate initial conditions? We apply this algorithm to explore those ceiling functions that appear as solutions to R(n). The pattern that emerges from this empirical investigation leads us to the following general result: every ceiling function of the form ceiling{n/q}$ is the solution of infinitely many such recursions. Further, the empirical evidence suggests that the converse conjecture is true: if ceiling{rn/q} is the solution generated by any recursion R(n) of the form above, then r=1. We also use our ceiling function methodology to derive the first known connection between the recursion R(n) and a natural generalization of Conway's recursion.Comment: Published in Journal of Difference Equations and Applications, 2010. 11 pages, 1 tabl

Large-Mass Ultra-Low Noise Germanium Detectors: Performance and Applications in Neutrino and Astroparticle Physics

A new type of radiation detector, a p-type modified electrode germanium diode, is presented. The prototype displays, for the first time, a combination of features (mass, energy threshold and background expectation) required for a measurement of coherent neutrino-nucleus scattering in a nuclear reactor experiment. The device hybridizes the mass and energy resolution of a conventional HPGe coaxial gamma spectrometer with the low electronic noise and threshold of a small x-ray semiconductor detector, also displaying an intrinsic ability to distinguish multiple from single-site particle interactions. The present performance of the prototype and possible further improvements are discussed, as well as other applications for this new type of device in neutrino and astroparticle physics (double-beta decay, neutrino magnetic moment and WIMP searches).Comment: submitted to Phys. Rev.

Prospects of cold dark matter searches with an ultra-low-energy germanium detector

The report describes the research program on the development of ultra-low-energy germanium detectors, with emphasis on WIMP dark matter searches. A threshold of 100 eV is achieved with a 20 g detector array, providing a unique probe to the low-mas WIMP. Present data at a surface laboratory is expected to give rise to comparable sensitivities with the existing limits at the $\rm{5 - 10 GeV}$ WIMP-mass range. The projected parameter space to be probed with a full-scale, kilogram mass-range experiment is presented. Such a detector would also allow the studies of neutrino-nucleus coherent scattering and neutrino magnetic moments.Comment: 3 pages, 4 figures, Proceedings of TAUP-2007 Conferenc

Glacial Discharge and its Impact on Phytoplankton Taxonomic Composition in an Antarctic Fjord

The influence of glacial discharge on phytoplankton community composition remains an open question. The Antarctic Peninsula fjords offer an ideal system to understand the effect of ice-ocean forcing on phytoplankton community, providing an extreme in the spatial gradient from the glacio-marine boundary to the Western Antarctic Peninsula (WAP) continental shelf. In Andvord Bay, we found that glacial meltwater input altered surface salinity and was enriched in dissolved iron and nitrate, supporting phytoplankton biomass. The three major groups of phytoplankton fueled by glacial input were: cryptophytes, diatoms, and a group of unidentified small flagellates. In December, cryptophytes dominated the phytoplankton community and were correlated with relatively warmer temperatures in the surface layer; in addition, contrary to our hypothesis, no diatom bloom was observed in the fjord in spite of dissolved iron concentration >1 nM. By April, after the growth season, the overall phytoplankton abundance had decreased by an order of magnitude. Phytoplankton, in particular diatoms, were then limited by daytime length despite abundant macro-nutrient and iron concentrations. Mixed flagellates emerged as the dominant group during April due to the decline of other major taxa. Deep-learning algorithms for predicting the abundance of each major phytoplankton group captured the effects of these environmental factors on the phytoplankton community. Our results show that the fjord, under the influence of glacial meltwater, has relatively high phytoplankton biomass combined with high macro- and trace nutrient concentrations when compared to other WAP regions influenced by sea ice melting. Based on this study, we confirm that flagellates can be the dominant taxon in Antarctic fjords and we propose that iron concentration alone is insufficient to predict diatom growth. Furthermore, buoyant meltwater plumes can enrich the fjord with nitrate even if the main circulation is not driven by glacier meltwater discharge. As glacial meltwater continues to alter the phytoplankton taxonomic composition, it will have an important implication for higher trophic levels and add significant uncertainties to the prediction of regional ecosystem dynamics and biogeochemistry.Fil: Jack Pan, B.. University of California at San Diego. Scripps Institution of Oceanography; Estados UnidosFil: Vernet, Maria. University of California at San Diego. Scripps Institution of Oceanography; Estados UnidosFil: Manck, Lauren. University of California at San Diego. Scripps Institution of Oceanography; Estados UnidosFil: Forsch, Kiefer. University of California at San Diego. Scripps Institution of Oceanography; Estados UnidosFil: Ekern, Lindsey. University of California at San Diego. Scripps Institution of Oceanography; Estados UnidosFil: Mascioni, Martina. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. División Ficología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Barbeau, Katherine. University of California at San Diego. Scripps Institution of Oceanography; Estados UnidosFil: Almandoz, Gaston Osvaldo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. División Ficología; ArgentinaFil: Orona, Alexander James. Ocean Motion Technologies; Estados UnidosOcean Sciences Meeting 2020Estados UnidosOcean Sciences Meetin

CoGeNT Interpretations

Recently, the CoGeNT experiment has reported events in excess of expected background. We analyze dark matter scenarios which can potentially explain this signal. Under the standard case of spin independent scattering with equal couplings to protons and neutrons, we find significant tensions with existing constraints. Consistency with these limits is possible if a large fraction of the putative signal events is coming from an additional source of experimental background. In this case, dark matter recoils cannot be said to explain the excess, but are consistent with it. We also investigate modifications to dark matter scattering that can evade the null experiments. In particular, we explore generalized spin independent couplings to protons and neutrons, spin dependent couplings, momentum dependent scattering, and inelastic interactions. We find that some of these generalizations can explain most of the CoGeNT events without violation of other constraints. Generalized couplings with some momentum dependence, allows further consistency with the DAMA modulation signal, realizing a scenario where both CoGeNT and DAMA signals are coming from dark matter. A model with dark matter interacting and annihilating into a new light boson can realize most of the scenarios considered.Comment: 24 pages, 12 figs, v2: published version, some discussions clarifie

Direct Search for Low Mass Dark Matter Particles with CCDs

A direct dark matter search is performed using fully-depleted high-resistivity CCD detectors . Due to their low electronic readout noise (RMS ~ 7 eV) these devices operate with a very low detection threshold of 40 eV, making the search for dark matter particles with low masses (~ 5 GeV) possible. The results of an engineering run performed in a shallow underground site are presented, demonstrating the potential of this technology in the low mass region

Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H2_{2}

A model of the collisional kinetics of energetic hydrogen atoms, molecules, and ions in pure H$_2$ discharges is used to predict H$_\alpha$ emission profiles and spatial distributions of emission from the cathode regions of low-pressure, weakly-ionized discharges for comparison with a wide variety of experiments. Positive and negative ion energy distributions are also predicted. The model developed for spatially uniform electric fields and current densities less than $10^{-3}$ A/m$^2$ is extended to non-uniform electric fields, current densities of $10^{3}$ A/m$^2$, and electric field to gas density ratios $E/N = 1.3$ MTd at 0.002 to 5 Torr pressure. (1 Td = $10^{-21}$ V m$^2$ and 1 Torr = 133 Pa) The observed far-wing Doppler broadening and spatial distribution of the H$_\alpha$ emission is consistent with reactions among H$^+$, H$_2^+$, H$_3^+$, and H$^-H$ ions, fast H atoms, and fast H$_2$ molecules, and with reflection, excitation, and attachment to fast H atoms at surfaces. The H$_\alpha$ excitation and H$^-$ formation occur principally by collisions of fast H, fast H$_2$, and H$^+$ with H$_2$. Simplifications include using a one-dimensional geometry, a multi-beam transport model, and the average cathode-fall electric field. The H$_\alpha$ emission is linear with current density over eight orders of magnitude. The calculated ion energy distributions agree satisfactorily with experiment for H$_2^+$ and H$_3^+$, but are only in qualitative agreement for H$^+$ and H$^-$. The experiments successfully modeled range from short-gap, parallel-plane glow discharges to beam-like, electrostatic-confinement discharges.Comment: Submitted to Plasmas Sources Science and Technology 8/18/201

Results from a Search for Light-Mass Dark Matter with a P-type Point Contact Germanium Detector

We report on several features present in the energy spectrum from an ultra low-noise germanium detector operated at 2,100 m.w.e. By implementing a new technique able to reject surface events, a number of cosmogenic peaks can be observed for the first time. We discuss several possible causes for an irreducible excess of bulk-like events below 3 keVee, including a dark matter candidate common to the DAMA/LIBRA annual modulation effect, the hint of a signal in CDMS, and phenomenological predictions. Improved constraints are placed on a cosmological origin for the DAMA/LIBRA effect.Comment: 4 pages, 4 figures. v2: submitted version. Minimal changes in wording, one reference adde