Spaces of finite element differential forms

We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit commuting projections. We present two families of spaces in the case of simplicial meshes, and two other families in the case of cubical meshes. We make use of the exterior calculus and the Koszul complex to define and understand the spaces. These tools allow us to treat a wide variety of situations, which are often treated separately, in a unified fashion.Comment: To appear in: Analysis and Numerics of Partial Differential Equations, U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, eds., Springer 2013. v2: a few minor typos corrected. v3: a few more typo correction

A computer program for a line-by-line calculation of spectra from diatomic molecules and atoms assuming a Voight line profile

Computer program predicts the spectra resulting from electronic transitions of diatomic molecules and atoms in local thermodynamic equilibrium. The program produces a spectrum by accounting for the contribution of each rotational and atomic line considered

Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length

We extend previous work on applying the epsilon-expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio xi = mu/epsilon_F of chemical potential to ideal gas Fermi energy to next-to-next-to-leading order (NNLO) in epsilon=4-d, where d is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO.Comment: 28 pages, 14 figure

Predicting the outcome of renal transplantation

ObjectiveRenal transplantation has dramatically improved the survival rate of hemodialysis patients. However, with a growing proportion of marginal organs and improved immunosuppression, it is necessary to verify that the established allocation system, mostly based on human leukocyte antigen matching, still meets today's needs. The authors turn to machine-learning techniques to predict, from donor-recipient data, the estimated glomerular filtration rate (eGFR) of the recipient 1 year after transplantation.DesignThe patient's eGFR was predicted using donor-recipient characteristics available at the time of transplantation. Donors' data were obtained from Eurotransplant's database, while recipients' details were retrieved from Charite Campus Virchow-Klinikum's database. A total of 707 renal transplantations from cadaveric donors were included.MeasurementsTwo separate datasets were created, taking features with <10% missing values for one and <50% missing values for the other. Four established regressors were run on both datasets, with and without feature selection.ResultsThe authors obtained a Pearson correlation coefficient between predicted and real eGFR (COR) of 0.48. The best model for the dataset was a Gaussian support vector machine with recursive feature elimination on the more inclusive dataset. All results are available at http://transplant.molgen.mpg.de/.LimitationsFor now, missing values in the data must be predicted and filled in. The performance is not as high as hoped, but the dataset seems to be the main cause.ConclusionsPredicting the outcome is possible with the dataset at hand (COR=0.48). Valuable features include age and creatinine levels of the donor, as well as sex and weight of the recipient

Solar particle history: 1983 version

It has long been known that the great majority of nuclear active solar particles are emitted in a few large storms in each 11 year cycle. A single storm in August 1972 dominated the fluence of particles of energy >10 MeV. Such storms can occur, it seems, at any time within the more active half ot the cycle. On a time scale long compared to 11 years, the knowledge comes from two sources. Terrestrial C-14 sets limits on the largest proton bursts that can have taken place in the 8000 years. Lunar surface samples have yielded data on mean fluxes on a time scale from the C-14 to the Mn-53 mean life. A mean flux was found of 70 protons >10 MeV and a rigidity constant R sub o = 100 MV to be robust on the 1,000,000 to 10,000,000 year time scale. Over the shorter periods represented by C-14 and Kr-81 the fluxes seem to have been higher by a factor of roughly three. Some examples of dating are discussed

Measurements of long-lived cosmogenic nuclides in returned comet nucleus samples

Measurements of long lived cosmic ray produced radionuclides have given much information on the histories and rates of surface evolution for meteorites, the Moon and the Earth. These nuclides can be equally useful in studying cometary histories and post nebular processing of cometary surfaces. The concentration of these nuclides depends on the orbit of the comet (cosmic ray intensity changes with distance from the sun), the depth of the sampling site in the comet surface, and the rate of continuous evolution of the surface (erosion rate of surface materials). If the orbital parameters and the sampling depth are known, production rates of cosmogenic nuclides can be fairly accurately calculated by theoretical models normalized to measurement on lunar surface materials and meteoritic samples. Due to the continuous evaporation of surface materials, it is expected that the long lived radioactivities will be undersaturated. Accurate measurements of the degree of undersaturation in nuclides of different half-lives allows for the determination of the rate of surface material loss over the last few million years

Investigation of double beta decay with the NEMO-3 detector

The double beta decay experiment NEMO~3 has been taking data since February 2003. The aim of this experiment is to search for neutrinoless ($0\nu\beta\beta$) decay and investigate two neutrino double beta decay in seven different isotopically enriched samples ($^{100}$Mo, $^{82}$Se, $^{48}$Ca, $^{96}$Zr, $^{116}$Cd, $^{130}$Te and $^{150}$Nd). After analysis of the data corresponding to 3.75 y, no evidence for $0\nu\beta\beta$ decay in the $^{100}$Mo and $^{82}$Se samples was found. The half-life limits at the 90% C.L. are $1.1\cdot 10^{24}$ y and $3.6\cdot 10^{23}$ y, respectively. Additionally for $0\nu\beta\beta$ decay the following limits at the 90% C.L. were obtained, $> 1.3 \cdot 10^{22}$ y for $^{48}$Ca, $> 9.2 \cdot 10^{21}$ y for $^{96}$Zr and $> 1.8 \cdot 10^{22}$ y for $^{150}$Nd. The $2\nu\beta\beta$ decay half-life values were precisely measured for all investigated isotopes.Comment: 12 pages, 4 figures, 5 tables; talk at conference on "Fundamental Interactions Physics" (ITEP, Moscow, November 23-27, 2009

Spin-Correlation Coefficients and Phase-Shift Analysis for p+3^3He Elastic Scattering

Angular Distributions for the target spin-dependent observables A$_{0y}$, A$_{xx}$, and A$_{yy}$ have been measured using polarized proton beams at several energies between 2 and 6 MeV and a spin-exchange optical pumping polarized $^3$He target. These measurements have been included in a global phase-shift analysis following that of George and Knutson, who reported two best-fit phase-shift solutions to the previous global p+$^3$He elastic scattering database below 12 MeV. These new measurements, along with measurements of cross-section and beam-analyzing power made over a similar energy range by Fisher \textit{et al.}, allowed a single, unique solution to be obtained. The new measurements and phase-shifts are compared with theoretical calculations using realistic nucleon-nucleon potential models.Comment: Submitted to Phys. Rev.

Dynamical stability of a doubly quantized vortex in a three-dimensional condensate

The Bogoliubov equations are solved for a three-dimensional Bose-Einstein condensate containing a doubly quantized vortex, trapped in a harmonic potential. Complex frequencies, signifying dynamical instability, are found for certain ranges of parameter values. The existence of alternating windows of stability and instability, respectively, is explained qualitatively and quantitatively using variational calculus and direct numerical solution. It is seen that the windows of stability are much smaller for a cigar shaped condensate than for a pancake shaped one, which is consistent with the findings of recent experiments.Comment: 23 pages, 11 figure